I noticed that the function onLookupDone is actually doing the same thing as onLookupTrigger, where the contents of the function are running on lookup rule startup instead of end.
After noticing this within Laserfiche forms, I took another look at the documentation and noticed that the handler for both functions is the same. Both stating:
"handler: The function to call when a lookup is triggered."
I attached a picture of the documentation below.