How do I troubleshoot a lockup that occurs when plugging in an external monitor?

Question

Since installing Lion, nearly every time I plug my 13" MacBook Air into my 27" Dell display, the Mac locks up. (The mouse pointer stops moving.) I can't do anything except shut it down and reboot.

How do I troubleshoot this?

Update: It looks like my DELL U2711 is broken...

I got a kernel panic on my MBA, and since rebooting, each time I plug in the Mini DisplayPort cable the display shows a DisplayPort icon and then goes into power saving mode. The same thing happens when I try Detect Displays on my MBA.

I tried a different DisplayPort cable (full-size DisplayPort plug on each end) with my DELL laptop running Windows 7, and saw the same problem. And then same thing happens when I try Detect Displays.

So it appears the problem is with my cable or my MBA, but the display.

Nonetheless, it's still an Apple hardware and/or software bug if my MBA locks up when I connect a defective monitor. But it's unlikely to be fixed since it's unlikely to be reproduced by an Apple engineer.

Update #2: I got a new DELL U2711 display (which works with my MBA using a the Mini DisplayPort cable). My MBA is locking up again when I plug the cable in, unless I reboot first and plug in before logging in.

I submitted Problem ID 10259810 on https://bugreport.apple.com/.

Update #3: I just tried connecting the DEL U2711 without rebooting first, now that I'm running OS X 10.7.3: my MBA did not lock up. (They may have fixed it prior to 10.7.3—I haven't tried to reproduce this problem for quite a long time.)