If I read this correctly, this is the first time you've run the TV on battery alone?
If this is the case, then the TV has had shore power until this time, and has not been running off the inverter.
The lines are a result of electronic "noise" in the power from the inverter. If you look
HERE , you'll find that the inverter creates a quasi-sine wave. You will need to have an inverter that creates a true sine wave unless someone else in the forum knows a trick I do not.
Road Trip America has a pretty decent write up to help decide which inverter to buy.
Here is another link that somewhat explains the difference between the two inverter types.
If the inverter and TV were provided by a dealer and you still have warranty coverage, talk to them about your findings. Bottom line, your TV is not compatible with a modified wave inverter.
Joe