Is there a way to suppress badge counts and the dock icon bounce for Terminal.app in Lion?
Google finds an example of what is, I think, disabling bounces for all Dock icons (not Terminal alone): 


Annoying infinite bounces of an icon on alert!!!

defaults write com.apple.dock no-bouncing -bool TRUE


However, that may be not the solution in this case. Puzzling me: 

[macbookpro08:~] gjp22% date
Tue  2 Aug 2011 13:40:41 BST
[macbookpro08:~] gjp22% uname -a
Darwin macbookpro08.centrim.freeman-centre.ac.uk 11.0.0 Darwin Kernel Version 11.0.0: Sat Jun 18 12:56:35 PDT 2011; root:xnu-1699.22.73~1/RELEASE_X86_64 x86_64
[macbookpro08:~] gjp22% defaults read com.apple.dock no-bouncing
2011-08-02 13:40:57.029 defaults[2501:303] 
The domain/default pair of (/Users/gjp22/Library/Preferences/com.apple.dock.plist, no-bouncing) does not exist


— nothing relating to no-bouncing my preference file, and I can run for example 

tail -f -n 50 /private/var/log/system.log

— then bring something other than Terminal to foreground, watch things added to the log and in my case: 


lines added to the background window do not cause any bounce, do not cause any count to appear in the Dock icon.