I know a lot of these get shot down so I'll understand if this does too :P
Why I think it works
Lakers: Get rid of Pau and the apparent chemistry issues, allowing Dwight to dominate the low post while acquiring a terrifically talented SF who I think can still get better. Gay will fit into a D'Antoni system and his athleticism (as a wing) and ability to play on the break is something lacking in LA. They also get Gooden to take minutes in the big-man rotation. Maybe have the artist formerly known as Ron Artest play some 4 as he's still a top level defender.
Grizzlies: This is a team just short of being a genuine contender, with this trade they shed some cap space (not much though). However they could start Allen as their best wing defender but have Ellis play serious minutes off the bench, he'd be the best 6th man in the league and is one of the most electric scorers around, can play some point at a pinch and can shift the offensive focus form ZBo/Gasol if need be.
Bucks: This is probably the thinnest hope but they do get to move Ellis to get one of the gunners out of their back court as well as getting an Pau - still a great player in the league though admittedly on the decline. I think this would benefit Jennings more than anything an he's the closest this franchise has to a future. Earl Clark can be a decent role player and is getting buried in LA; Selby can score and could be a (very) poor-man's Ellis replacement.
Feel free to comment/wildly abuse :)
Parts of this make sense, but it really only makes sense for the Lakers.
Agreed. I feel like Kupchak's ability to get deals done which totally favour the Lakers could help :P I don't know that it really lifts the Grizzlies to "genuine contender" status though. I do worry that Milwaukee are becoming one of those middle of the road teams that aren't going to be good enough to compete, or bad enough to get better through the draft; this is not a good place to be when your not an attractive free agent destination.