Please provide more details. Describe in detail exactly what happens or doesn't happen.
Also, if there is an error message, please quote the exact complete unedited word-for-word error messag.e
After updating OS X it is usually necessary to trash the prefs. Start by quitting Lightroom. Launch Finder and on the menu bar click “Go” whilst holding down the Optn(Alt) key and choose Library. Open the Preferences folder and trash the two plist files relating to LR3 (see image below which relates to LR6)
Then re-launch Lightroom.
N.B. Apple hides the user Library until the Alt key is depressed.