Lexus are known for their reliability. A colleague of mine recently clocked 275,000 miles in his 16 year old GS300. Costs to date have been limited to regular maintenance at his local dealer. No major fault to report and everything is working fine. Admittedly it is not a RX or indeed a hybrid, but it reflects well on the Lexus brand.
I would, however, get the car from a dealer to benefit from the warranty, and consider investing in an extended warranty as you suggest. I would also consider a service plan which will guarantee fixed monthly costs and a (approx.) 10% discount AND joining this forum to secure a further 15% discount on parts and labour... all this assuming that you will be getting your car serviced at your local dealer.
Dealers may not normally have high mileage cars on their forecourts, but may be willing to source one for you..
Have you checked the Lexus website? - There are currently 2 high milers in pretty good condition at the Southampton dealership. One is slightly above your budget, but I am sure you could talk them down...