Hi, I must tell you, I don't know what the heck Zap 1000's are, but I do know something about electricity.
There are two possibilities:
1. you are trying to power the lights off direct AC current. (This is the stuff that you get out of the outlet at your house.)
2. You are trying to recharge batteries that power the lights, in which case you are using DC current, which is the same as your car battery, your camera batteries,, etc.
Generators, except in extremely rare cases (read not-available) produce AC current, the same as in your house. This would work fine if you are directly powering the lights. As in the lights have a plug on them that plugs into the wall of your house.
If this is the case, then you could not hook them up to your car through a jumper cable type thing, because that is DC current.
BUT!
Instead of a generator, which is expensive, you could buy (and since you mentioned your car, I am assuming that your car is nearby) an Inverter. This is a device which usually has a plug which fits into cigarette lighter and which changes the DC power of your battery into AC power, which it outputs through a regular House-type outlet located on the device itself.
I use one of these regularly to power lights, radios, pumps, computers, etc. off my truck during extended stays in the desert.
Be forwarned: The AC power from your house is about 120 volts, the DC power from your car is 12 volts. Most electrical equipment is rated in Watts.
Volts times Amps = Watts
if your lights are 1200 Watts (and there is probably a little plate on your lights which will give you the watts, or the amps, etc.) then from your house volts (120) it takes 10 amps to make the light work. But from your car (12 volts) it would take 100 Amps! A Huge amount! This would be a Big inverter (read expensive) and would drain your car battery fairly quickly.
If you have a boat store, like a West Marine, somewhere close by, or an RV Center, call them and ask about inverters, they should be able to help.
Good Luck,
Whitney