I'm on a Windows machine with admin access, using Anaconda Navigator. I was successfully able to open JupyterLab in Firefox (not my default browser) by adding c.SeverApp.browser = '"C:\\Program Files\\Mozilla Firefox\\firefox.exe" %s' to jupyter_server_config.py however it launches in the default Firefox profile which I don't want. I'm unsure of how to get it to open in another profile.
Looking online I found c.LabApp.browser = 'firefox --profile /path/to/profile/directory %s' for an older version but even with some tweaks I was unable to get this to work. I also tried c.ServerApp.browser = '"C:\\Program Files\\Mozilla Firefox\\firefox.exe -P "profile"" %s' but it didn't work either. I'm have JupyterLab 4.2.5.
This will open the Firefox profile window and let you choose the profile.
c.ServerApp.browser = '"C:\\Program Files\\Mozilla Firefox\\firefox.exe" -P <profilename> %s'