The issue with that, though, is thanks to U-haul only equipping with a four prong harness, you'll only be able to power the lights on a trailer equipped with electric brakes. Unless the trailer has surge brakes - like all of the U-haul trailers do - then you're basically back into the same situation.
The brakes on the Lexus may be small for the towing weight, but at least any electric trailer brakes will aid. With a U-haul rental you'll have bigger brakes on the truck, but no trailer brakes.
If you go this route it may be worth it to rent the U-Haul trailer, too, just for the peace of mind of having brakes to go with it.