Generally it should be no problem as long as each new tire/rim combo has a load rating equivalent to or higher than half the maximum trailer weight, and so long as the tires don't rub on the trailer at full suspension compression. With a 2" lift already the second issue shouldn't be a problem. Keep in mind that the door step keeps getting further off the ground each increase in height - you've probably already seen this with the lift. The one negative is that the tires will probably wear somewhat quicker due to more weight on a smaller contact patch.
I run -2 size winter tires on my pickup here in the winter. The narrower tread does cut through snow better and provides more traction, but I'm not so sure there is any advantage to that on a trailer as traction is not really required. A small trailer like that is just going to follow along behind, and unless you have an undersized tow vehicle, I doubt that the tail would wag the dog much.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2018 Nissan Titan Midnight Ed.