@mycars Welcome to the world! There's really not much that can go wrong on these trucks. If it was me, I'd look at the chassis and evaluate the rust situation. This is purely my opinion, but there are too many of these that have never been up north to ever buy one that has been, even for a day. If we were talking about a 40, that would be a different conversation, but rust is a sin you can absolve without an awful lot of penance.
I have had my LX570 since 2012 and have replaced the starter, steering gearbox and rack (that's a design flaw, based on my conversations with Lexus, but I haven't heard of anyone else on 'Mud with the same complaint) and cam tower seals (a very common problem on Land Cruisers, but not LX570s). Of those, the olnly problem you could find on an inspection is the cam tower leak. The upper rear corner of the block will be oily.
I have three other complaints, which you can find during an inspection, very quickly and easily. First, the Peltier cooler (front seat heater/cooler) in the Gen I 200 series sucks and my DS seat element is toast. Toyota fixed this in the Gen II 200 series, by replacing that POS with a functional element. Still, check the heating function; it should fell like sitting on a hot steel deck in the sun. The cooling function should feel very cool. If either doesn't function noticeably, use that as a price negotiating point.
Second, check the AHS system. With the engine running and the transmission in park, the truck should move from N to H to L and back to N in seconds. If it doesn't the system may need new accumulators, but at 10 years, I'd doubt this would be a problem.
Last, check the 4WD function of the transfer case. This is one area I would negotiate a price reduction if you find it. There is a known design flaw in the actuator for the transfer case. It's a relatively easy fix, but it's time consuming and if it's not fixed, it will effectively disable the truck until it resolves itself (which it always has on mine; I haven't gotten around to fixing it yet because I don't wheel this truck).
You should be able to shift into LO from HI and back to LO without any noise (other than the slight actuator click you may or may not hear) and lock and unlock the center differential (it's the button you hit with your knee when you're getting in the seat )while idling in gear and driving straight,. This will happen more often when it's cold outside, so you may not see this in this weather, even if it's present, but check for it anyway.
If either function fails, driving backward and forward sometimes helps to clear the fault, as does stopping, putting the transmission in park and stopping and restarting the engine. The problem is the actuator sensor loses its place and can't determine whether the transfer case has actually shifted or not. The mechanical function is rock solid, but this little sensor is a problem child. The fix is well documented here. If you buy the truck and if it has this problem, I can help you with the fix.
Alternately, my 2008 LX570 is going to be on the market next month for somewhere around half this price (albeit with twice the miles, but it's a Land Cruiser, so mileage, in my opinion, really isn't a buying factor, as much as age and use would be) , so if you don't get this one, give me a call.
Good luck!