Hello and welcome to the forum.
You say your outlets work so you must be on shore power. The lights are 12 volts. First check the breaker for the converter. Then you need to check the converter output. If you installed a new battery and the lights worked for a while. Then it sure sounds like the problem is in the converter.
One more thing to check and it has happened to a few of us. When you replaced the battery did you hook it up correctly? If not the reverse polarity fuses may have blown they are 40 amp in most cases. Do you know if your converter is part of the power center or a deck mount/ by it self?
2009 Seville VF32KS
2019 GMC Sierra 3500HD Crew Cab Denali.
6.6 Diesel standard box.