I am having the same problem, but only when I try to connect my MacBook Pro (i7, 2010) to the LED Cinema Display 24". I also have a MacBook Air 11", and when I connect it to the display it works fine. So it's not that the Cinema Display is faulty.
The odd thing, however, is that I can connect the MBP to a HDTV without any problems. So it can't really be something wrong with the MBP, either.
It is just the combination MacBook Pro + Cinema display that doesn't work.
All other combinations work:
MacBook Air + Cinema Display = fine
MacBook Pro + HDTV = fine
(MacBook Air + HDTV = also fine)
The setup (MBP + Cinema Display) has worked fine for years. This issue only started a few weeks ago. I can't say if it started in connection to a specific software update of any kind or not, but I'm pretty sure it didn't.
Yesterday I even went so far as to do a clean install of Lion, but that did not work either.
If nothing else, I sincerely hope this issue goes away with Mountain Lion.