Welcome aboard! If the trailer is plugged into shore power, 120v, then the lights should work with or without good batteries if the converter is working correctly.
So check the battery disconnect switch first. If you can pull the key out it's off. It needs to be on so rotate the switch 180 degrees. Check that and let us know if that solves it.
Jeff & Sandi (and Teddy - 7lb Schnorkie)
2018 Montana High Country 305RL
2012 RAM 3500 Crew Cab 4x4 SRW
Demco Recon Hitch on B&W Turnover Ball