Lookup Fields can't be set as "Read Only"

Lookup Fields can't be set as "Read Only"

Hi - I am working with Users & Permissions and I have set some Look Up fields as "Read Only" for selected users. Unfortunately, these settings don't seem to work correctly.  While I can NOT change any other fields that is set up as "Read only", I can still modify Lookup Fields as well as file upload fields.  Any solutions on this?
Thanks,