I do not think it is the battery disconnect switch as twinboat says because things work on shore and alternator power.
Not knowing how you wired things up it's impossible to diagnose.
I did my upgrade to a '16 Bounder and did a lot of research.
My thread on it here:
'16 Bounder Lithium and Solar upgrade
My take on your problem has something to do with the BCC. You'll see a detailed wiring schematic in my post there. Not sure if it is a malfunction of that unit (or components inside of it) or a wiring problem.
Lights inside work on shore power because the converter (not the batteries) is providing 12v power.
Lights inside work when the engine is on because the alternator (not the batteries) is providing 12v power.
Are the lithium/house batteries being charged at all?