@Shashank -

Thanks for some of these links, the DMLException in a Catch method within the TestMethod is exactly what i was looking for. Now when the Exception matches the expected string I provided, it passes the test. Code snippet attached for help for others:

static testMethod void Trigger_LockinCheckAcctForStartUpPricingInsert3()
    {   
//
//Insert a Test Account with a Boolean field for validation parameters   
//
    test.startTest();
        try{
       
        Account a = new Account();
       
        a.Name = 'Test Lockin Account3';
        a.Start_Up_Pricing_Consumed__c = true;
       
    insert a;
       
//Insert child custom object with Status != Active or Approved
//but Parent Account pricing already consumed 
//     
    LockIns__c l = new LockIns__c();
       
        l.Account_for_lock_in__c = a.Id;
        l.Status__c = 'New';
        l.Start_Date__c = System.today();
            
    insert l;   

//Update the custom object record's "Status" to "Active" which will provide Validation Error
//because the Parent Account is already set to TRUE.
//       
        l.Status__c = 'Active';
       
    update l;
        }
        catch(Exception e){
            System.Assert(e.getMessage().contains('Validation Rule exception message goes here'));
        }
        test.stopTest();
    }