When firefox crashes, sometimes lock files are left over that prevent firefox from starting again.
If you are sure that you have no firefox running on any machine, but firefox still claims to be running, find the directory named
gi32rog@zuse:~/.mozilla/firefox/w6zn9vkj.default$
where "w6zn9vkj" will differ in your case, and delete the two files "lock" and ".parentlock"
-rw-r--r-- 1 gi32rog IntegraTUM 0 Dec 14 15:09 .parentlock lrwxrwxrwx 1 gi32rog IntegraTUM 20 Jan 18 11:19 lock
Now firefox should start again without an error message.