• Add a field to the Case object called "Fire Email" (Fire_Email__c api name)
• Create a Workflow Field Update
  • Setup > Build > Create > Workflow & Approvals > Field Updates > New Field Update button
  • Name: Whatever you want
  • Object : Case
  • Field To Update: Fire Email (The new field you just created)
  • Re-evaluate Workflow Rules : Uncheck this
  • Specify New Value: Choose False
  • Save
• Create Email Alert
  • Setup > Build > Create > Workflow & Approvals > Email Alerts > New
  • Description: Give it something desriptive of what the email we will be sending out will be.
  • Unique Name: Whatever you want
  • Object: Case
  • Email Template: Pick an email template you want to use (you might have to create one if you want something new for this scenario)
  • Recipient Type: For testing, select your user, once you have everything working come back and change it to the CEO.
  • Save
• Add a Workflow Rule on the Case object that will run if the Fire Email field is set
  • Setup > Build > Create > Workflow & Approvals > Workflow Rules > New > Select Case > Next
  • Name: whatever you want
  • Evaluate on: created, and any time it’s edited to subsequently meet criteria
  • Criteria: Fire Email equals true
  • Save & Next
  • Click "Add Workflow Action" > Select Existing Action
  • Set Search to Email Alerts
  • Find the Email Alert you just created, select it, then click the right arrow
  • Set Search to Field Update
  • Find the Field Update you just created, select it, then click the right arrow
  • Save
  • Click Done
  • On the page you get redirected to (The Workflow page) click Activate
• Now the fun part, create the trigger. You will have to do this on a sandbox and then deploy it to production.
• Login to Sandbox and go to Setup > Customize > Cases > Triggers > New
• Paste the following code, then click Save. I don't know the API name of the Lot field on the case so I just assumed it was Lot__c. If that is not the case, replace any mention of Lot__c in the code with the correct API name.
• After deploying the trigger to production, everything should be working correctly.

trigger trg_Case_FireEmailOn3rdCasePerLot on Case (before insert)
{    
    //get the lot numbers for all cases inserted
    Map<string, List<id>> lotToCasesMap = new Map<string, List<id>>();
    for(Case c : trigger.new)
    {
        if(!String.isBlank(c.Lot__c))
        {            
            if(!lotToCasesMap.containsKey(c.Lot__c))
            {
                lotToCasesMap.put(c.Lot__c, new List<id>());
            }
            
            List<id> temp = lotToCasesMap.get(c.Lot__c);
            temp.add(c.Id);
            lotToCasesMap.put(c.Lot__c, temp);            
        }
    }
    
    //Determine which lots have 2 or more cases in the last 45 days. We really care for 3, but the case being created would be the 3rd.
    List<AggregateResult> aggRes = [SELECT Lot__c lot, Count(ID) FROM Case 
                                    WHERE Lot__c IN :lotToCasesMap.keyset() AND CreatedDate = LAST_N_DAYS:45
                                    GROUP BY Lot__c
                                    HAVING COUNT(ID) >= 2];
                                    
    Set<string> lotsThatTrigger = new Set<string>();                               
    if(aggRes != null && aggRes.size() > 0)
    {
        for(AggregateResult a : aggRes)
        {
            system.debug(a.get('lot'));
            string lotNum = string.valueOf(a.get('lot'));
            lotsThatTrigger.add(lotNum);   
        }
        
        system.debug(lotsThatTrigger);
        for(Case c : trigger.new)
        {
            if(c.Lot__c != null && lotsThatTrigger.contains(c.Lot__c))
            {
                system.debug('here');
                c.Fire_Email__c = true;
            }
        }
    }
}