How to Add A User To A Database In Standby / Read-Only Mode In Sql Server
Check if the database is part of logshipping. As the database in secondary server will be in Read-only/standby state. ALtering the database directly will not be allowed.

Identify the primary server and add the user there. This will move to your read-only secondary.

Edit : 1

Make sure the logins exist in both the servers.