Compressed Backup size value is incorrect in msdb
This is just conjecture, but it sounds like LiteSpeed is compressing the backup after SQL Server has performed it's part of the work.  I doubt you can get accurate compression numbers from msdb in this scenario.

If Quest is using deduplication in their SQL Server backup product then SQL Server will certainly not be able to understand the real size of the backup, since the data stored in the backup will be opaque to SQL Server.

If you are trying to retain a history of backup sizes for growth tracking, you could use the numbers stored in MSDB as a rough guide to percentage growth over time.  If you need exact sizes of the backups saved by Quest LiteSpeed, I would recommend contacting Quest's technical support to see if there is a way to do that.