Making a (lookup) column editable on the record page only under specific conditions is possible with a help of business rules for a specific section.
As for the lookup (lookup object) itself it's possible to set column permissions for a specific user or roles as on the screenshot 1:
However, as of now, it's not possible to lock columns for a specific lookup dynamically (after adding the record to a lookup itself) with a help of basic system tools.
We have registered a corresponding query for our R&D team and will be awaiting for the implementation of the mentioned functionality in the upcoming versions.
