With Windows Explorer or the Mac Finder, go to the folder containing the Lightroom catalog - usually inside the Pictures or My Pictures folder.
There will be a file with the extension .lock
Delete this file, do not delete anything else. Now try to launch Lightroom.
The lock file is something that is generated whenever Lightroom is opened, and it is usually deleted automatically when Lightroom is closed. However, if Lightroom shuts down abnormally for some reason, that lock file can be left behind. It's necessary to delete it manually, and then you can continue working with Lightroom.