Good question. My answer is that I want whatever will bring quality back to the company again. This means I would never want quality product like Lilo to fail, unless I could be sure this failure would actually encourage more quality projects later on.
I hope that Lilo is widly successful so that we can then watch Eisner's next move. If he looks at these projects like Lilo and say "Gee, quality really does sell", then starts up more projects like them, then all is well. If not, then I say toss him, since the man would have demonstrated one final time that he can't observe what makes the company successful.
I realize that tossing him under these conditions violates your precondition (I wasn't given that option), but I beleive that is the only logical way to approach the problem. To answer your question any other way requires a gift of precognition that I do not have. I would have to know if the sacrifice of Lilo (resulting in Eisner's departure), would actually result in more quality projects futher on. I think the odds would be higher for this to happen, but there is no way to be sure.