This could also be iOS related in that some older O/S can't load newer version of Browsers. Did you check into that as well? I do know from Windows that FF57 will not load on anything lower then W7 so there is a limit to how far back a Browser can load on older O/S.

If there a problem with updating or with the permissions then best is to download the full version and trash the currently installed Firefox application to do a clean reinstall.

Download a new copy of the Firefox application and save the Disk Image file to the desktop

• Firefox 57.0.4: *https://www.mozilla.org/en-US/firefox/all/

• trash the currently installed Firefox application (open the Applications folder in the Finder and drag the Firefox application to the Trash) to do a clean reinstall
• install the new version that you have downloaded
• https://support.mozilla.org/en-US/kb/Installing+Firefox+on+Mac

Your personal data like bookmarks is stored in the Firefox profile folder, so you won't lose personal data When you uninstall and reinstall or update Firefox, but make sure NOT to remove personal data When you uninstall Firefox as that will remove all Firefox profile folders and you lose your personal data.

WestEnd said

This could also be iOS related in that some older O/S can't load newer version of Browsers. Did you check into that as well? I do know from Windows that FF57 will not load on anything lower then W7 so there is a limit to how far back a Browser can load on older O/S.

iOS which is used on say iPad/iPhone has nothing to do with this. The OP appears to have OSX 10.12 which meets the minimum of OSX 10.9+ for Firefox 49.0 to current.