It could be your LED Ceiling lights (If installed) are interferring with your HDTV set. This is a known RFI problem with using some brands of LED lights especially using the OTA Antenna on the roof that is picking up weaker HDTV signals...
The only other thing I can think of is maybe your battery is very low and just enough juice to run the small converter powering up the TV set. Then when you turn on the ceiling lights it drains the battery down enough more to knock off the Power Inverter... This might be especially true if you are using standard automotive type bulbs in your ceiling lights. Each incandescent 12VDC bulb in the fixtures draw around 1AMP each.
???
Roy Ken