Why can't Mail.app send email on Lion?
My grandmother's computer had the same issue. After trying a bunch of stuff, I ended up deleting the IMAP account and re-added it and everything works fine now.

As commented, you could also use the connection doctor (search for it in help if you can't find it under the menu structure for Mail) and see that all of the servers and passwords are set up correctly. Often an old setting can go stale or the preference file could get corrupt and need a new password to be stored for the sending side of email.