If you've got a charging system with a battery, then the draw on the battery will only be the difference between the load and generated electricity.
For example...let's use a 100W draw from the lights.
If your stator is producing 130W, then 30W is allocated to charging the battery while the other 100W goes to the lights.
If your stator is only producing 80W, then 20W will come from the battery to total 100W going to the lights.
Granted, that's not taking into account inefficiencies or anything, but it gives you a general idea about what's going on.

If you have a 5Ah battery used with a 130W stator and 100W lights, it will take 2 hours to fully charge your battery.
If you turn the lights off and use 100% of the stator's 130W to charge the battery, it'll get a full charge in 30-45min.

As for the battery eventually going down without a charging system, yeah...obviously LOL
However, think of it as a fuel tank for your lights.
If you're riding all day at the dunes, you need a few gas cans back at camp to refuel, right?
Just make a stop and fill up your tank.
Same way with the batteries...have a few back at camp that are charged and/or rotated out on the charger.
During your refueling, swap out the battery for a fresh one and hook the used one up to a charge.
If your fuel tank is only going to let you ride for 2hrs, then you only need a battery that will provide a 2hr run time.
A charging system is worthless if you don't have the fuel to run the stator.
3 cell lipo batteries can be fully charged in 10-30min depending on brand and type, so by the time you fuel up your quad, grab something to drink, and cool off for a few minutes, your lipo should be fully charged again.
Take a spare if you want to run the lights longer than you'll be riding, or as a precautionary measure.
And FYI, the lipo batteries are pretty much any size you want...5,000mah battery=5Ah battery, a little smaller than a motorcycle battery, and you can plug them up in series just like diesel truck batteries to get more capacity.
All depends on how long you want to run the lights, or how much light you want as to the size of the battery that'll work best.