The steps below guide you through setting the configuration files required for Firefox to not only turn off updates, but deny the setting entirely. Also note, this is on a per computer basis. This process will need to be replicated on each computer/server as necessary or desire.
Note: The install directories used here is default for a Windows 64-bit operating system. You install path may different.

Create file local-settings.js in C:\Program Files (x86)\Mozilla Firefox\defaults\pref

Copy the following and save in file

pref("general.config.obscure_value", 0);

pref("general.config.filename", "mozilla.cfg");

Create file mozilla.cfg in C:\Program Files (x86)\Mozilla Firefox

// lockPref("app.update.auto", false);

lockPref("app.update.enabled", false);

Test and confirm access
You can confirm this by going to the Preferences and Update tab and find that the update options are greyed out. Alternatively, browse to about:config and the above options will be in Italics.

If the above solution doesn't work, you can also try:
https://support.mozilla.org/en-US/questions/963728