Delete definitely a message from Mail
There is a several hundred word long tutorial, 

Full Step-by-Step Tutorial  taken from here, that I have used to solve this problem so in addition to the author testing it, I too have things fully working.

Here are the steps from the article as well as details from the two key steps.

Step 1: Configure Apple Mail preferences  

Step 2: Assign mailbox functions

Step 3: Set the [Gmail]/ prefix on custom labels

Step 4: Designate which labels show in IMAP

Since this is the most important step, here are the details


  While you’re in the Labels tab, uncheck the “Show in IMAP” box for All
  Mail because you don’t want that showing up in Apple Mail anymore.
  This is important to ensure the delete button sends messages to the
  Trash in Mail.app. The “Show in IMAP” box will determine which labels
  appear in Apple Mail. Feel free to uncheck the “Show in IMAP” box for
  any other labels while you’re at it. Changes are saved automatically.


Step 5: Forwarding and POP/IMAP

This also is a key step where google allows you to delete a message once it's removed from tha “last visible IMAP folder.” By hiding the All Mail label in IMAP, there should only be one “visible” copy of your message, so when you delete the message in Mail, it will now move the message to the Trash.



Step 6: Restart Apple Mail

Step 7: Test it out

I've tested this on Lion 10.7.5 and works perfectly.
All images are from Jeff Schuette as is the quoted text explaining how google can be set up to work like all the rest of the Mail servers to delete messages when you trash them.