Read only/Standby database - Set user permissions
The user has to be granted permissions in the source copy of the database.

The restored copy is just that -- a copy -- of the source, so there's no way to change one and not the other.

Since this is a SQL Server login, you'll need to create the logins on both servers with identical SIDs so the mapping from the database user to the login matches in all cases. You can do this by recreating the login on the secondary, specifying the SID manually in the CREATE LOGIN statement.

If you went with a solution such as replication (not saying you should, just giving an example), this works using two read/write databases, where you could grant permissions completely independently.