Does that mean my Zoom should not be in lock down mode?

Hi An17gels,

welcome o the Apple (user-to-user) Community.

Re: "Does that mean my Zoom should not be in lock down mode?"

As we are all Apple users, like yourself, in the Community, unless someone with the technical skills, or one of the very few with actual experience using Lock down mode, answers, most of us may not be able to advise you. Your question surely deserves some response, however.

Apple support's online article (link below) gives the available info.

Lock down your Mac if targeted by a cyberattack - Apple Support

And their other article does provide the choice of whether to "exclude" particular apps and websites from lock down mode if you wish:

About Lockdown Mode - Apple Support

Re: Zoom error code 10004 : seems to have been a problem with automatically installing Zoom updates;

Good to know you solved that issue ok by just manually installing the latest version of the desktop client .

All the best :-)