2. Updates shows LimeChat with a grayed out "Installed" [one expects it to say Update]
3. Click Purchases "Update". LimeChat downloads and now shows "Installed"
4. Click Updates "Update" [yes, it has changed]. LimeChat downloaded and now shows "Installed"
Go back to step 3 until you tire of this.
The copy on SnowLeopard needs updating, but App Store is updating the up-to-date copy on the boot volume, so the old copy still needs updating. Booting SnowLeopard and running App Store would likely update the old copy.
$ cd /tmp
$ strings /Volumes/SnowLeopard/Applications/LimeChat.app/Contents/_MASReceipt/receipt > old
$ strings /Volumes/MountainLion/Applications/LimeChat.app/Contents/_MASReceipt/receipt > new
$ diff old new
Pro, OS X Mountain Lion, early 2011 2.3GHz 16GB