LSN numbers query regarding Differential backups
While not exactly answering your LSN questions, I think you definitely need to revisit your Recovery Point Objective (RPO).  How much data are you willing to lose?  Assuming good hourly differentials, you should be able to restore back to the latest hour (currently), but you wouldn't really be able to take advantage of any transaction log backups. I'd definitely suggest increasing the frequency of transaction log backups - maybe every 15 minutes.  If they take 10 minutes to complete, then that would most likely be the most data you'd lose - assuming your other backups are good (full and diff).

All backups have enough of the log to be able to restore a consistent database by applying committed changes after the backup started and rolling back transactions that had not completed before the backup completed. 

Check out Paul Randal's excellent post on Understanding Logging and Recovery in SQL Server.