LimitedUser needs permissions on Database2 to do whatever the stored procedure is doing in that database, ownership chaining will only work within the same database (unless you enable the server option Cross Database Ownership Chaining, which I don't recommend as it breaks down the database container as a security boundary).
So, for example, you have db1 and db2, there is a stored proc in db1 that executes select * from db2.dbo.table1
For this you need LimitedUser to have:
- execute permissions in the db1 database for the procedure
- select permissions on table1 in db2