I did similar-paid up front deposit without seeing the car from main Lexus dealer 150 miles away but with the promise it would be refundable if not as described.
Well I am generally pleased with the outcome and they sent me an online video beforehand of the car to help make up my mind.
Yes you can get a good deal privately if you have the 'readies' available and having spoken to the previous owner of my car, Lexus put 50% on top of the price they gave him in cash as he was retiring and didn't want a p/ex.
However a decent p/ex for my old car and a 12 months approved warranty made the decision to buy easier.
There are many cars out there with Lexus and from my experience there can be a marked difference between each franchise as to what you get for your money.If not happy-walk away or at least insist on a refundable deposit if the work agreed is not to standard.
Just my thoughts.