Where are the following backup file properties Recovery Model, Backup Type, Name, Description, lsn numbers and Destination being kept?
They are stored on the system database MSDB under the following tables dbo.backupfile, dbo.backupfilegroup, dbo.backupmediafamily, dbo.backupmediaset and dbo.backupset.
select * from msdb.dbo.backupfile
Note that this does not include information on compressed size and Backup Timing.
See the following tables on the LiteSpeedLocal and LiteSpeedCentral for such details: