This happens when Firefox has crashed or has not shut down properly (i.e. logging out before closing your browser).
You need to delete the lock files in order to run Firefox. These files are normally removed when Firefox closes. However, when the browser fails to shut down properly, they need to be manually deleted.
The lock files are stored in your .mozilla directory with your profile data. There are usually two lock files named lock and .parentlock.
To find the lock files, run these commands from your home directory:
find . -name *lock
Once you delete these lock files, you will be able to run Firefox.
If this doesn't solve your problem, we recommend deleting your .mozilla directory so a fresh set of configuration files will be created the next time your run Firefox. If you want to save your bookmarks, you can rename your .mozilla directory to old.mozilla and import your bookmarks from your old profile.