Check if database is restored to the most recent log file
You should be able to use the restorehistory table on the server to which you are restoring to get the most recently restored LSN.

SELECT TOP 1 b.type, b.last_lsn
 FROM msdb.dbo.restorehistory a
 INNER JOIN msdb.dbo.backupset b 
     ON a.backup_set_id = b.backup_set_id
 WHERE a.destination_database_name = 'YourDatabaseName'
 ORDER BY restore_date DESC


This was posted in a discussion of log files some years ago at: http://www.sqlbackuprestore.com/logsequencenumbers.htm

EDIT: As a further option, if you are using Enterprise Edition you can use database snapshots for reporting.  The database in this case remains in restore mode and the snapshot(s) read only.  If this is your environment, you could indeed use log shipping to keep your Reporting Server data up to date.