An uninterruptable power supply (UPS) is mainly designed to ensure smooth power to racks of computers while the power is on, and has a small amount of backup battery for power failures. The system you need is generator -> charger -> battery during the day, and battery -> DC/AC inverter -> LED lights at night. Your UPS includes a battery, charger, and inverter, so in theory it will work.
It looks like you have this model
which contains an 8.5 Amp-hour battery. This is pretty tiny as far as batteries go -- most camps use beefy marine batteries which are ten times the size. It also contains a built-in charger which I expect would automatically refill the batteries when the unit is plugged in to the generator, but it says recharge time is sixteen hours.
8.8 amp-hours at 12 V is 100 Watt-hours. This means you can run a single 20 foot strand of LED christmas lights (5 to 10 watts) for 10 to 20 hours on this battery on a full charge. From that page it sounds like the unit might contain two batteries, and you have two units, so that means you get four strands of light (enough to dimly light your camp) for 10-20 hours, or else fewer strands for longer. Each hour of recharging would give you another hour of light at night (1:1). If you only have the lights on for a couple hours a night and you have a pretty small amount of them it should work fine. But I would just try it out and test it.