Your RV uses the COACH battery for a number of electrical items, including your interior lights.
Your COACH battery must be kept fully charged for these items to work properly. Regardless of whether you are using external AC Power or your built-in generator, the battery is kept charged by your CONVERTER which in turns uses your 110-VAC.
As to using LED interior lights, if you purchased the proper LED replacement lamps that are marked with the same lamp number on them then they should operate properly, But, there is one thing about LED lamps; they are either ON or OFF. They do not operate but seem dim on a low voltage, like incandescent lamps do.
From your symptoms, I would suspect your COACH battery.