Engine Exhaust System problems of the 2002 Lexus RX300

I have a Lexus Rx300 2002 which I purchased used because of their well know reputation to operate for a long time. Two weeks ago our mechanic noticed our oil down a quart and did a oil change and asked us to watch oil level. 300 miles later it was down again. We were referred to take it to a Lexus dealer to have the problem checked out. There is a recall for oil gel for 1999 to 2002. Well ours had no signs of oil gel, but it is engine related. They can not tell us what the problem is until they take the engine completely apart. The referred us to Lexus for a goodwill reimbursement because of the high cost to fix the engine. We sent all our records of oil changes and it took Lexus 4 days to get back to us with a offer of they will pay for the parts and we pay for the labor of approx. $3,100. 00. I have read about the Lexus engines of those years having problems and I feel it is a mechanical defect from the factory. Our car has 56,000miles and I am told the engine is just breaking in. I feel I have a lemon and I need some help because I am having a problem accepting their offer. . .