I think Pierce for Pau makes a lot of sense for both clubs and both players.
Lakers & Pierce: Pierce settling in as a 2nd option behind Kobe, usually against the opponent's lesser wing defender, would really improve his efficiency, and he's such a good complementary player with his shooting and passing. A big upgrade on MWP in that role (and MWP going to the bench as a combo forward behind Pierce and Clark kicks the dreadful Antawn Jamison out of the rotation). Pierce is also a pretty easy-going teammate - been chummy with Kobe in the past and pretty content to "give the game what it needs" as a 3rd banana.
The Lakers would take a hit to their center rotation, with no true size other than Sacre behind Howard. Perhaps we could throw in Wilcox - a nice fit with D'Antoni.
There's also the fact that Pierce does nothing to address their age/speed problem. But I think adding high-impact talent is more important consideration to the Lake Show than just getting younger and faster.
Pau & Celtics: Pau is just a dream fit for Doc, KG and the Celtic's offense. Doc is absolutely dedicated to getting the ball into the post and KG is a great compliment to a post-oriented big like Pau with his elite mid-range game and high post passing. Pau to makes KG more dangerous in the post by drawing the bigger defender and boasting a brilliant passing/facilitating skillset of his own. Then you have the always accommodating Rondo who will work to feed Gasol in his preferred spots. Pau also would give us a nice boost on the boards compared to Bass/Collins, and decent shot-blocking as well.
Bringing in Pau would bring up some issues defensively - we'd get slower moving KG to the 4 alongside Pau at the 5 (though with how slow Bass has been playing this year, I don't think it would be much of a drop off). We'd also be left with Green as our only wing defender with size and pretty slim pickings in free agency to back him up.
Offensively, the downgrade from Pierce to Green hurts already tenuous floor-spacing, but I like Green, Lee and Bradley enough from the corners and Terry from anywhere to be comfortable.