Copy of Firefox already open....

Hello Françoise, The explanation is given here:
http://kb.mozillazine.org/Profile_in_use

In short and clearly, you normally just need to delete the file named .parentlock

This file is here:
Hard Drive / Users / your_name / Library / Application Support / Firefox / Profiles / xxxx.default / .parentlock

You are on Lion, so your library may not be as directly accessible as under 10.6, but by navigating up the directory tree from the Finder's toolbar you can reach it. (I created a shortcut in the sidebar for that..)

Then, to make things a little more tricky, this file to delete (it blocks your profile and assumes you already have a Firefox window open due to corruption), must be made visible so you can throw it away. To make files visible/invisible, you can use the Hidden Files widget or Onyx (it has a Lion version).
With the widget, it’s a bit less immediate than under Snow Leopard; you may sometimes need to relaunch Finder from the Dock, but it eventually works and is faster than with Onyx.

Tell me the result..

Have a good day :)

PS: another method is to delete the entire Firefox folder after making sure to recover your bookmarks, then put these bookmarks back into the new folder that will be automatically recreated:
Hard Drive / Users / User_Name / Library / Application Support / Firefox / Profiles / bookmarks.html


Always indicate your EXACT CONFIGURATION: Mac model and Mac OS version!
Francis Sanspseudo - iMac Intel Mac running OS 10.7 + iMac-G5 running Mac OS 10.5