The most plausible theory by far is that he was basically shelved after Capone went to prison; they just didn't have any use for him. He was more of a thug than big earner and there were a few other reasons that I can't really remember. He tried to make a living playing golf as he was really good but it didn't work out. Eventually he started going back to "the boys" demanding some action and pointing out how much dirt he had on everybody, which led to Nitti giving the order to have him killed. The building where he was killed on Milwaukee and Chicago is still standing. And his girlfriend, the famous "Blonde Alibi" Louise Rolfe was probably one of the last Capone era players to die; she died in the 90s. (Geraldo famously interviewed her.)
The other theory is that he was killed in retaliation for something, such as the St. Valentine's Day Massacre (he didn't participate but may have planned) but as far as I know no one really believes that.
The Green Mill was his night club at one point and as you probably know is the only true Capone-era nightclub still open.
They made a whole movie out of the Joe E. Lewis thing that happened there with Sinatra as Lewis called "The Joker's Wild"
For at least a year McGurn was acting paranoid. Before he was killed a government agent witnessed him at a sit-down in Florida and saw other high-level Outfit mobsters with him. So I would guess that McGurn did or said something serious, or at least was accused of doing something serious. Demanding action and making threats would probably qualify. Don't think it would have been Nitti giving the order if he wasn't the boss. If he was with Grand Avenue it would have been Capezio and his bosses Campagna and Ricca.
