As I was writing the instructions below, I saw that the problem was solved by restarting your mac - Great!
FCP X uses "lock files" to prevent a library being accidentally used by different users simultaneously, and these sometimes can prevent one from accessing a library. The solution I was about to offer deletes lock files, in case they have become corrupted and prevent legitimate access to your libraries. Offered "as is", and should never be done without a BACKUP in place.
------- No longer necessary, but just in case it may help someone, I leave those here anyway ---
0) Backup your library (always!)
1) Quit FCP X if it is running (just in case)
2) Control-click on a library in the Finder and choose Show Package Contents
3) Press Command-Shift-period to make Finder show hidden files
4) Delete one or more of the following: .lock, .lock-info, .lock-dir