This all hinges on A. Sheed + a late 1st being a better offer than Courtney Lee (nope) and B. Ariza being willing to accept a bench role (very unlikely).
I'd love Ariza on this team in theory but I don't think you can say Danny could've made this deal and just chose not to for no apparent reason.
A. Lee himself was a late 1st rounder just a couple of seasons ago. He's a solid player, not exactly the greatest late round pick.
The last five draft classes with an NBA track record, of players drafted between picks 20 - 30 that match or surpass Courntey Lee's talent or value:
2004 - Jameer Nelson, Delonte West, Tony Allen, Kevin Martin, Anderson Varejão
2005 - Nate Robinson, Jarrett Jack, David Lee
2006 - Rajon Rondo, Kyle Lowry, Jordan Farmar
2007 - Jared Dudley, Wilson Chandler, Rudy Fernández, Aaron Brooks
2008 - Ryan Anderson, Courtney Lee, George Hill
2009 - Darren Collison, Omri Casspi, Taj Gibson
So no, I don't think it's that easy to say it's Lee over a Celtics first rounder
for a non-contending team. Also, a draft pick is more economical for a team looking to rebuild.
B. Ariza doesn't have a no trade clause.
I think Ainge balked at the idea of adding salary beyond the 2012 season and was probably trying to steal Battier instead.