Create a custom db roles that uses a lookup table
Roles need to be explicitly defined. You can't tell the engine to just look up the role membership and/or rights in a table.

You'll need to manually create the roles/permissions with dynamic SQL from the table, and come up with some kind of plan to keep them in sync whenever the data in the table changes (you can use a trigger or, if a delay is possible, a scheduled job).

You mention schemas, and I'm not sure how relevant that is, but obviously an easier way to manage this would be to put all of the relevant users in a role, put all the relevant objects in a schema, and GRANT permissions on the schema to the role. If you have exceptions you can implement DENY.