Create Apex Class Controller.

Apex class [customLookUpController.apxc]

public class customLookUpController {
    @AuraEnabled
    public static List < sObject > fetchLookUpValues(String searchKeyWord, String ObjectName) {
        system.debug('ObjectName-->' + ObjectName);
        String searchKey = searchKeyWord + '%';
        
        List < sObject > returnList = new List < sObject > ();
      
        // Create a Dynamic SOQL Query For Fetch Record List with LIMIT 5   
        String sQuery =  'select id, Name from ' +ObjectName + ' where Name LIKE: searchKey order by createdDate DESC limit 5';
        List < sObject > lstOfRecords = Database.query(sQuery);
        
        for (sObject obj: lstOfRecords) {
            returnList.add(obj);
        }
        return returnList;
    }
}

• In above Apex class we have only one @AuraEnabled Method.
• In this method we have 2 String ‘searchKeyWord’ and ‘ObjectName’ parameter.
• By this parameter we are find sObject record List and Return the list.

 Step 2 : Create Lightning Event

• Next we create a Lightning Event bundle for communicate data(attribute values) between different components. (Child To Parent Component )
• Events are contain attributes that can be set before the event is fired and read when the event is handled by component.

from developer console >> file >> new >> Lightning Event >> enter name >> selectedsObjectRecordEvent >> save

lightning Event [selectedsObjectRecordEvent.evt]

<aura:event type="COMPONENT" description="by this event we are pass the selected sObject(lookup list record) in the parent component">
    <aura:attribute name="recordByEvent" type="sObject"/>
</aura:event>

• In above Event we have only single attribute which type is sObject type.
• by this attribute, we are passing the selected Object record to parent component [ CustomLookup ]  by child component[customLookupResult ].

Component Blue Print 

Step 3 : Create Child Component For Display the Search Result List

Lightning Component [customLookupResult.cmp] 

<aura:component implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global">
	<aura:attribute name="oRecord" type="sObject" />
        <aura:attribute name="IconName" type="string"/> 
 
  <!--Register the component level event-->
    <aura:registerEvent name="oSelectedRecordEvent" type="c:selectedsObjectRecordEvent"/>
 
    <li role="presentation" class="slds-listbox__item" onclick="{!c.selectRecord}">
        <span id="listbox-option-unique-id-01" class="slds-media slds-listbox__option slds-listbox__option_entity slds-listbox__option_has-meta" role="option">
              <span class="slds-media__figure">
                  <span class="slds-icon_container" title="Description of icon when needed">
                    <lightning:icon iconName="{!v.IconName}" class="slds-icon slds-icon_small" size="small" alternativeText="icon"/>
                    <span class="slds-assistive-text">Description of icon</span>
                  </span>
              </span>    
              <span class="slds-media__body">  
                  <span class="slds-listbox__option-text slds-listbox__option-text_entity">{!v.oRecord.Name}</span>
              </span>
        </span>
    </li>
</aura:component>

({
   selectRecord : function(component, event, helper){      
    // get the selected record from list  
      var getSelectRecord = component.get("v.oRecord");
    // call the event   
      var compEvent = component.getEvent("oSelectedRecordEvent");
    // set the Selected sObject Record to the event attribute.  
         compEvent.setParams({"recordByEvent" : getSelectRecord });  
    // fire the event  
         compEvent.fire();
    },
})

Step 4 : Create Lightning Custom Lookup Component [Parent]

Lightning Component [customLookup.cmp]

<aura:component controller="customLookUpController" implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global">
    <!--declare attributes--> 
    <aura:attribute name="selectedRecord" type="sObject" default="{}" description="Use,for store SELECTED sObject Record"/>
    <aura:attribute name="listOfSearchRecords" type="List" description="Use,for store the list of search records which returns from apex class"/>
    <aura:attribute name="SearchKeyWord" type="string"/>
    <aura:attribute name="objectAPIName" type="string" default=""/>
    <aura:attribute name="IconName" type="string" default=""/>
    <aura:attribute name="label" type="string" default=""/>
    <aura:attribute name="Message" type="String" default=""/>
    
    <!--declare events hendlers-->  
    <aura:handler name="oSelectedRecordEvent" event="c:selectedsObjectRecordEvent" action="{!c.handleComponentEvent}"/>
   
    
    <!-- https://www.lightningdesignsystem.com/components/lookups/ --> 
    
    <div onmouseleave="{!c.onblur}" aura:id="searchRes" class="slds-form-element slds-lookup slds-is-close" data-select="single">
        <label class="slds-form-element__label" for="lookup-348">{!v.label}</label>
        <!--This part is for display search bar for lookup-->  
        <div class="slds-form-element__control">
            
            <div class="slds-input-has-icon slds-input-has-icon--right">
              <lightning:icon class="slds-input__icon slds-show" iconName="utility:search" size="x-small" alternativeText="search"/> 
                <!-- This markup is for when an record is selected -->
                <div aura:id="lookup-pill" class="slds-pill-container slds-hide">
                     <lightning:pill class="pillSize" label="{!v.selectedRecord.Name}" name="{!v.selectedRecord.Name}" onremove="{! c.clear }">
                          <aura:set attribute="media">
                             <lightning:icon iconName="{!v.IconName}" size="x-small" alternativeText="{!v.IconName}"/>
                          </aura:set>
                      </lightning:pill>
                </div>
                <div aura:id="lookupField" class="slds-show">
                    <span class="slds-icon_container  slds-combobox__input-entity-icon" title="record">
                        <lightning:icon class="slds-icon slds-icon slds-icon_small slds-icon-text-default" iconName="{!v.IconName}" size="x-small" alternativeText="icon"/>
                        <span class="slds-assistive-text"></span>
                    </span>
                    <ui:inputText click="{!c.onfocus}" updateOn="keyup" keyup="{!c.keyPressController}" class="slds-lookup__search-input slds-input leftPaddingClass" value="{!v.SearchKeyWord}" placeholder="search.."/>
                </div>   
            </div>
        </div>
        <!--This part is for Display typehead lookup result List-->  
        <ul style="min-height:40px;margin-top:0px !important" class="slds-listbox slds-listbox_vertical slds-dropdown slds-dropdown_fluid slds-lookup__menu slds" role="listbox">
            <lightning:spinner class="slds-hide" variant="brand" size="small" aura:id="mySpinner"/>
            <center> {!v.Message}</center>
            <aura:iteration items="{!v.listOfSearchRecords}" var="singleRec">
                <c:customLookupResult oRecord="{!singleRec}" IconName="{!v.IconName}"/>
            </aura:iteration>
        </ul>
    </div>
</aura:component>

({
   onfocus : function(component,event,helper){
       $A.util.addClass(component.find("mySpinner"), "slds-show");
        var forOpen = component.find("searchRes");
            $A.util.addClass(forOpen, 'slds-is-open');
            $A.util.removeClass(forOpen, 'slds-is-close');
        // Get Default 5 Records order by createdDate DESC  
         var getInputkeyWord = '';
         helper.searchHelper(component,event,getInputkeyWord);
    },
    onblur : function(component,event,helper){       
        component.set("v.listOfSearchRecords", null );
        var forclose = component.find("searchRes");
        $A.util.addClass(forclose, 'slds-is-close');
        $A.util.removeClass(forclose, 'slds-is-open');
    },
    keyPressController : function(component, event, helper) {
       // get the search Input keyword   
         var getInputkeyWord = component.get("v.SearchKeyWord");
       // check if getInputKeyWord size id more then 0 then open the lookup result List and 
       // call the helper 
       // else close the lookup result List part.   
        if( getInputkeyWord.length > 0 ){
             var forOpen = component.find("searchRes");
               $A.util.addClass(forOpen, 'slds-is-open');
               $A.util.removeClass(forOpen, 'slds-is-close');
            helper.searchHelper(component,event,getInputkeyWord);
        }
        else{  
             component.set("v.listOfSearchRecords", null ); 
             var forclose = component.find("searchRes");
               $A.util.addClass(forclose, 'slds-is-close');
               $A.util.removeClass(forclose, 'slds-is-open');
          }
	},
    
  // function for clear the Record Selaction 
    clear :function(component,event,heplper){
         var pillTarget = component.find("lookup-pill");
         var lookUpTarget = component.find("lookupField"); 
        
         $A.util.addClass(pillTarget, 'slds-hide');
         $A.util.removeClass(pillTarget, 'slds-show');
        
         $A.util.addClass(lookUpTarget, 'slds-show');
         $A.util.removeClass(lookUpTarget, 'slds-hide');
      
         component.set("v.SearchKeyWord",null);
         component.set("v.listOfSearchRecords", null );
         component.set("v.selectedRecord", {} );   
    },
    
  // This function call when the end User Select any record from the result list.   
    handleComponentEvent : function(component, event, helper) {
    // get the selected Account record from the COMPONETN event 	 
       var selectedAccountGetFromEvent = event.getParam("recordByEvent");
	   component.set("v.selectedRecord" , selectedAccountGetFromEvent); 
       
        var forclose = component.find("lookup-pill");
           $A.util.addClass(forclose, 'slds-show');
           $A.util.removeClass(forclose, 'slds-hide');
  
        var forclose = component.find("searchRes");
           $A.util.addClass(forclose, 'slds-is-close');
           $A.util.removeClass(forclose, 'slds-is-open');
        
        var lookUpTarget = component.find("lookupField");
            $A.util.addClass(lookUpTarget, 'slds-hide');
            $A.util.removeClass(lookUpTarget, 'slds-show');  
      
	},
})

({
	searchHelper : function(component,event,getInputkeyWord) {
	  // call the apex class method 
     var action = component.get("c.fetchLookUpValues");
      // set param to method  
        action.setParams({
            'searchKeyWord': getInputkeyWord,
            'ObjectName' : component.get("v.objectAPIName")
          });
      // set a callBack    
        action.setCallback(this, function(response) {
          $A.util.removeClass(component.find("mySpinner"), "slds-show");
            var state = response.getState();
            if (state === "SUCCESS") {
                var storeResponse = response.getReturnValue();
              // if storeResponse size is equal 0 ,display No Result Found... message on screen.                }
                if (storeResponse.length == 0) {
                    component.set("v.Message", 'No Result Found...');
                } else {
                    component.set("v.Message", '');
                }
                // set searchResult list with return value from server.
                component.set("v.listOfSearchRecords", storeResponse);
            }
 
        });
      // enqueue the Action  
        $A.enqueueAction(action);
    
	},
})

.THIS .leftPaddingClass {
    padding-left: 2rem;
}
 
.THIS .pillSize{
 width:100%;
}

<aura:application extends="force:slds">
  <!-- Create attribute to store lookup value as a sObject--> 
  <aura:attribute name="selectedLookUpRecord" type="sObject" default="{}"/>
 
  <c:customLookup objectAPIName="account" IconName="standard:account" selectedRecord="{!v.selectedLookUpRecord}" label="Account Name"/>
 <!-- here c: is org. namespace prefix-->
</aura:application>

This is a dynamic Re-Usable Lightning Component you have need to pass the objectAPIName , IconName, selected Recordand Field Label Name Attribute when use this Custom Lookup component.

How to Use –  Example Custom Lookup Component

Now we are create a simple and small Lightning Component to create Contact Record Using custom Account Lookup and Name field.

Apex Controller 

public class contactSaveCtrl {
 @AuraEnabled 
    public static void saveContact(Contact con){
        insert con;
    }   
}

<aura:component controller="contactSaveCtrl" implements="force:appHostable,flexipage:availableForAllPageTypes,flexipage:availableForRecordHome,force:hasRecordId,forceCommunity:availableForAllPageTypes,force:lightningQuickAction" access="global">
    <aura:attribute name="selectedLookUpRecord" type="sObject" default="{}"/>
    <aura:attribute name="objContact" type="contact" default="{'sobjectType':'contact'}"/>
  
  <div class="slds-m-around_large">
      <ui:inputText class="slds-input" value="{!v.objContact.LastName}" label="Last Name"/>
 
      <c:customLookup objectAPIName="account" IconName="standard:account" label="Account Name" selectedRecord="{!v.selectedLookUpRecord}"/>
      
<br/> 
      
    <button class="slds-utton slds-button_brand" onclick="{!c.saveContactRecord}">Save Contact</button>    
  </div>       
</aura:component>

({
	saveContactRecord : function(component, event, helper) {
        var conObj = component.get("v.objContact");
           //set the default accountId is null 
           conObj.AccountId = null ; 
       // check if selectedLookupRecord is not equal to undefined then set the accountId from 
       // selected Lookup Object to Contact Object before passing this to Server side method
        if(component.get("v.selectedLookUpRecord").Id != undefined){
          conObj.AccountId = component.get("v.selectedLookUpRecord").Id;
        } 
        
       //call apex class method
      var action = component.get('c.saveContact');
        action.setParams({
            'con': conObj
        })
      action.setCallback(this, function(response) {
        //store state of response
        var state = response.getState();
        if (state === "SUCCESS") {
         alert('Record Created');
        }
      });
      $A.enqueueAction(action);
        
       
	}
})