It wouldn't be patients lawsuits. In reality the hospital would've sacked House out of pressure from insurers. Why is it this one hospital has such high per patient cost? And they would figure it's just House skewing the costs everywhere because of his tendency to order every single test in the lab's catalog and MRIs to all his patients. At least it makes sense when his patients are celebrities and billionaires. But otherwise every patient treated by him not on the outpatient clinic, probably left that hospital bankrupt.

Not so much donations as Cuddy considers him a "necessary evil" for the greater good - he's expensive, irresponsible and kind of an asshole, but genius enough to get away with it because otherwise People Would Die. Even in season 1 (I think), Business Guy Chi McBride takes over as chairman and wants to axe the whole department because it's that much of a money sink.