Groupon stock only has to hold its value long enough for his lockout (usually 6 months) to end. It's usually not hard to do that - when things come crashing down, it's usually a few years in the future, not months.
Not really. Unloading 20% of a company without telling anyone is both hard and, I think, illegal (as an exec). This is one of the reasons Bill Gates' stock sales are so consistent is to keep the market from freaking out when he sells stock. (Ohmigod, Bill sold stock! Oh wait, he's done that every month for 10 years... nevermind.)
Lefkofsky might be able to hedge against the decline of the stock, but hedging 20% of a big company (especially because it'd be difficult to build a portfolio which replicated Groupon's situation and risks) is a pretty tall order.
All that said, I tend to agree with your sentiment...