First a few questions so I can narrow down this issue rather than throw a list of possibilities. What Windows are you currently running(Vista, 7, 8, 10 etc) and when you say "update" you are talking about a Windows Update, not an upgrade to 10 or 8?
Those questions out of the way, it sounds like the program is being restored in startup rather than being opened when you click it (sometimes can happen when the computer hibernates instead of shutting off, it will try to reopen the last programs that were closed as a convenience to the user. You can try manually killing the process in task manager
(CTRL-ALT-DEL and select "Task Manager" navigate to the "processes" tab and look for a process specifically for the lightroom program, or in "programs" tab under running programs. Select it and click "end task" click "end task" again on the popup, do not restart, attempt to load the program)
It is also possible that the program is no longer compatible with your windows version. (Uninstall and re-install the program to correct)
Bad Windows update: See the following link for instructions on how to remove the update in windows 7, I will link more specific instructions if this is not your system. :)