Ok, you have 3 things to improve your code/post.

1. Use code box to post your code

When you post your post, you see an brief case with "C" icon in the editor at the top. If you use it, the code is posed as code and it looks prettier. So, I'll copy and paste yours for my post.

2. isInsert = true section - insert records at once

So, you define List<Event> lgaEvents out of the loop. I guess you saw it in someone's code.

The reason is, to save the # of DML statement. You can actually execute only 20 DML statements (insert/update/delete) in 1 execution (including triggers/workflows triggered by the trigger), so inserting a record one by one is not a good idea (Trigger.new could have up to 200 records).

And insert/update/delete accept an object and List, so you can actually do insert lgaEvent;.

List<Event> lgaEvents = new List<Event>();
if(trigger.isinsert)
for (LGA__c lga : System.Trigger.new){
Event event = new Event(
StartDateTime = lga.LGA_Start_DateTime__c ,
EndDateTime = lga.LGA_End_Date_Time__c,
Subject = 'LGA Scheduled',
IsRecurrence = FALSE,
Description = lga.Event_Description__c,
Location = lga.Event_Subjects__c,
Event_ID__c = lga.Event_ID__c,
IsAllDayEvent = False);
lgaEvents.add(event);
insert lgaEvents;
}

if(lgaEvents.size() > 0) insert lgaEvents;

}else{
....
}

3.  Query records at once

The # of Query is also up to 20 in 1 execution, so as you said, you need to save the # of query.

If you are a developer for Java or any other language, you may think this is weird, but if it is about the governor limit, you also should use the gorverner limit for your good.

The point is, you use "WHERE - IN" clause to get all required records at once. the "IN" clause accept List and Set so SFDC expects us to use it. Define a Set (to avoid duplication) to hold all Event_ID__c to query, and use it for "IN" clause. Since the Trigger.new has up to "only" 200 records due to the limit of max batch size, the Set won't have more than 200 IDs in this case. Well, that's not so bad.

For your convenience, you should put the query result to Map<Id, Event> so that you can easily get the Event object by Event_ID__c.

And you don't update the record one by one.

Set<Id> idSetEvent = new Set<Id>();
for (LGA__c lga : System.Trigger.New) {
idSetEvent.add(lga.Event_ID__c);
}
Map<String, Event> evMap = new Map<String, Event>();

for(Event ev :[
SELECT
id, Event_ID__c
FROM
Event
WHERE
Event_ID__c in :idSetEvent
]){

evMap.put(ev.Event_ID__c, ev);

}

for (LGA__c lga : System.Trigger.New) {
Event event = evMap.get(lga.Event_ID__c);
if(event == null){
// do something like event.addError('Event ID is wrong');
continue;
}
event.StartDateTime = lga.LGA_Start_DateTime__c;
event.EndDateTime = lga.LGA_End_Date_Time__c;
event.Subject = 'LGA Scheduled';
event.Description = lga.Event_Description__c;
event.Location = lga.Event_Subjects__c;
lgaEvents.add(event);
}
if(lgaEvents.size() > 0) update lgaEvents;

 ThomasTT