Fire javascript/jquery event after search is completed

Try putting that $.ajaxComplete JS block into a custom component exactly named "last_chance_html". This will be inserted AFTER the native Lithium JavaScript stuff.

Which probably is the reason you cannot catch the AJAX requests made by Lithium Code, your code is inserted BEFORE and therefore executed BEFORE the native Lithium JS code, so your event "catcher" doesn't listen to events registered later on in the code...