You could add a condition to the trigger that checks the object to see if the object exists, or is already lit. You could set a variable and add the condition to see if it is already set.
Or use the system event, "Trigger Once while true."
Lots of ways, but they depend on your events. But actually you sound like you may have most of that covered, in that everything you were checking is destroyed.
Could you make a small demo capx that works similar to what you are doing that we can make suggestions for?