I would call Lexus customer service ASAP and see if there's anything that they can do for you. They may be able to provide some assistance before you go shopping a new engine. You never know.

http://www.lexus.com/contact/

 

The dealership is trying to hold you liable for the issue; like you said, there's no way 6qts of oil leaked or burnt up in the motor in that short amount of time. I'm holding up my BS flag on that one!

 

Given the recent major engine work that was done on the car, I would go in and talk to the dealership service manager. If he/she is no joy then call Lexus and tell them you consider the recent engine repairs are responsible for the failure.