Travel trailers are pretty awful as far as trailers go - high polar moment, high frontal area, poor aerodynamics, high COG, and relatively short tongue to axle vs load distribution ratio. Basically all the worst things you could come up with in one package.
But the LX should be able to tow a midsize one pretty well. On paper it matches up pretty comparably to my last F250. I had an 06 F250 crewcab diesel 4x4. Awful truck - like unbelievably awful reliability. But it towed pretty darn well. When it was running... Anyway the LX700 has more power, more torque, is heavier, has similar brake size. AHC should be excellent at locking down the suspension and self leveling. I do question if Toyota tuned it correctly for that use to firm up enough. Pretty much everything except the overall rear suspension design (narrow spring spacing) and the short wheelbase (probably the biggest issue here) points to a pretty solid tow vehicle.
I know this is the LX forum - but might be worth noting here that Toyota appears to be building a more legit raptor competitor. Some spy shots going around. Looks like maybe 37s on the test mule. If they do a matching Sequoia it might be the size up off-roader some of us with families have wanted. Wouldn't hold my breath for Toyota to actually build it.