Can you describe the lines a little better?
The most likely thing I can think of, assuming that you are using the same tv as before you moved, is a ground loop problem. Either the cable tv, or out of the outlets your xbox or tv are plugged into may not be properly grounded. This is especially likely if it is an older apartment building.
Typical symptoms are moving diagonal lines, and a slight humming noise at 60Hz from the speakers. Try disconnecting your cable tv connection and any other unneeded devices that hook up to the tv, and see if that helps. It does on mine. Search google for "ground loop" and you'll find plenty of information. If it turns out that your electrical or cable systems aren't properly grounded, you should complain about it because it can be a safety hazard (if any equipment gets damaged and shorted to the case you could get a nasty shock).
If you have the xbox hooked up through any other devices (vcr or something), and you have rca inputs on your tv, try hooking it up directly. Another common problem is the really cheap switches that have inputs for all your gaming systems so you don't have to swap cables. They can pick up a lot of interference.