Traversing related List - Error

Question

trigger ABCD on Account(after insert, after update) {
    List < Account > AccList = [Select id, (Select Id, Status__c from Clients__r) from Account WHERE Id IN: trigger.new];
    for (Account acc: AccList) {
        Integer Field1 = 0;
        for (Client__c pc: acc.Clients__r) {
            If(Status__c != 'Lapsed') {
                Field1=Field1+1;
            }
            acc.Field1__c = Field1;
        }
    }
}

Purpose -

I want to increase the count of a people in the object Account which has a lookup with another object. So I want to traverse the related list records, check if a field value is equal to lapsed, if No - increase the count.

Error -

Didn't understand relationship 'LookupNameinAccount__r' in FROM part of query call. If you are attempting to use a custom relationship, be sure to append the '__r' after the custom relationship name. Please reference your WSDL or the describe call for the appropriate names.

Question -

1. I was reading articles on the relationship name . But not sure what exactly I need to use . I am currently using the name in the Fields section .
2. Is this code overall okay?

Answer 1

You cannot do this directly with one trigger. Because it will gives the Recursion if you use the Update DML directly

Try the below procedure

Apex Class (Which will be used to stop the Execution of Trigger more than once)

public class RecursiveClass {
    public static boolean updateOnce = false;
}

Apex Trigger

trigger ABCD on Account (after insert, after update) {
    if(RecursiveClass.updateOnce == false){
        RecursiveClass.updateOnce = true;
        List<Account> AccList = [Select id, Field1__c, 
                                        (Select Id, Status__c 
                                   from Clients__r) from Account WHERE Id IN: trigger.new];
        List<Account> updateList = new List<Account>();
        Integer demoField = 0;
        for (Account acc: AccList) {
            for (Client pc: acc.Clients__r) {
                 /* Change the Status based on your condition because In coding you given 
                 Not equal to 'Lapsed' but in Explanation you have given 
                 Equal to 'Lapsed'. Change that according to your scenario.
                 */
                If(pc.Status__c != 'Lapsed') {
                    demoField++;
                }
            }
            acc.Field1__c = demoField;
            updateList.add(acc);
        }
        if(updateList.size()>0){
            update updateList;
        }
    }
}

Hope this might helps...