The only answer to that is either maybe or it depends. The lights won't be the only drain on your batteries and the solar panel may not charge all of the loss to the battery(ies) if it is cloudy or you use more than 50 watts. Keep in mind that the fridge uses electricity as does all the alarms built into the unit. If you use the furnace you are using BUNCH of juice. The water pump also runs off of the battery bank as well.
You need to figure the actual power use on a daily basis to determine if you are really charging the battery bank up or just getting a partial charge. You also need to figure how many amp hours you have in the battery bank as well. One battery at "X" hours or a combination of 2 or more batteries at "X" amp hours.
I can guarantee that if you use more than 50 watts the batteries will go down until they are dead or you charge them back up and that is assuming the solar panel is really putting 50 watts into the battery bank.
Mike Nancy and the fuzzies
Fulltiming since June 2004
Volvo 660 MH tow vehicle
2005 MS 38RL
2007 Saturn Ion "toad"
2010 Gold Wing "piggyback"