Answer:
If you get a message like "Firefox is already running, but is not responding. To use Firefox, you must first close the existing Firefox process, restart your device, or use a different profile" that means you have a lingering Firefox browser running on another machine, for example in the AT labs, or within a Remote Desktop session.
If possible you should cleanly end that session before starting a new one. If that's not possible and you wish to leave the current session untouched then you can launch firefox from a terminal window like this:
firefox -P &
which will give you the option to create an alternative empty profile.
Otherwise, you can simply delete the lock file which firefox creates. From a terminal window run the command:
rm -f ~/.mozilla/firefox/*/.parentlock