Lights work off the 12 volt system. Could be as easy as your battery is hooked up wrong, which, will cause the converter to cut out when on shore power. You have two electrical systems in your rig, one for 120 volts and one for 12 volts. Outlets, AC, MW, operate off 120 volts most of the rest off the 12 volt system.
2011 Toyota Tundra double cab