Battery for the interior lights for at night

I would say so, unless you need your generator for something like the air conditioner. It seems like a wast of fuel and a lot of noise for the benefit of having power if you decide you want to turn on a light in the middle of the night.

Another benefit if you tow the trailer is it will need the battery to activate the emergency breakaway switch if the trailer becomes disconnected. This will put the trailer brakes on in a disconnect situation and hopefully keep the trailer from crossing into incoming traffic and killing someone.