If I try to quit Firefox when it's "Looking up domain.com..." it beachballs (hangs), goes into "not responding" status, then finally quits. It does this without fail.
This is on Mac with the latest FF, but it's always been this way for me, even on Windows with FF and I've noticed it with other applications.
Is there any technical reason why this can't be handled better?
No. You can use threads or even seperate processes to do this asynchronously (non-blocking). This is just poorly written software.
Aside from that, I don't have this particular problem with FF...
I haven't noticed anything with FF/windows XP, but this might help:
http://installingcats.com/2008/06/05/slow-internet-with-leopard/
Leopard had some well-documented DNS problems earlier this year, you can search for blog posts /forums
You should check bugzilla.mozilla.org to see if there are any recent bugs regarding the DNS service. Historically, this type of problem is very rare in Firefox and other mozilla based products, but there have been times where specific problems caused the DNS service to die or wait until a timeout.
The other important question is: are you sure it is DNS? A packet trace or necko debug logs might be useful. The way the status bar works, what is says is not necessarily what is keeping it from quitting.
There is a bug report for this problem. It has been around since at least 2004.