On the Rovers? Mostly just the real expensive shit dealing with electrical issue on the older vehicles, and drivetrain/motor related parts(4WD parts). They are rock solid vehicles compared to all the other SUV stuff on the road and if you plan to do any real offroad use(major camping, trail riding , etc) they are certainly the way to go.
Most of my experience does deal with them out/beyond warranty service though so buying new with a warranty will cover you for those first good years no doubt.
Parts for them are just really expensive. You’ll hear people say how BMW’s and Porsche’s are expensive but ANYTHING british will tower above those in maintenance costs in the latter years if things are let go too long. The guy who bought my last 944 owns a nice range rover and spent almost 2.5K having me repair broken exhaust header studs(in the heads) because it required an engine removal to do so.
I’ve never looked at an LR2 so I can’t speculate or comment on the vehicle itself. New, I’d imagine it’s a very good vehicle and it’s highly probable that it will outlast the BMW and related counterparts by a long shot as long as it’s taken car of. I think the new Range Rovers are a good looking vehicle. Maybe I’ve just had a continuous string of bad work related knowledge towards them and it’s made me a bit biased against buying one.