Interesting question... ;-) I haven't seen any option to "lock" the mixer. You can only create and load a user profile, which by default restricts access to • System Settings • Audio Routing Options • Input Source Patching • UCNET Options • Scene Lock / Unlock. Additionally you can restrict access to • Channel / Bus Names • Channel Types • Input EQ/Dynamics • Output EQ/Dynamics • Preamps • GEQ • Assigns • Changing FX Types • Save Scenes • Changing / Adding DCA Filter Groups.
Additonally and most important, Level Limit (maximum level for the Main bus) can be adjusted/fixed between -84 dB and +10 dB. Setting volume to -84 means to turn Main volume off. When the user profile is selected, the Main fader moves down immediately. This looks like a good way to "lock" the mixer, at least the audio of Main Out. Restricting access to flex mixes seems not to be possible.
When the user profile "No Access To Anything" is selected, all above mentioned functions are also deactivated in UC Surface. No access to EQ, gain, main volume, nothing... It still says FOH permission selected in Settings, but everything in UC Surface is inactive.