Litespeed does not store anything additional over what is stored by native backups in msdb.
With that said, Litespeed can be configured to stored history in a repository which is either local or remote. If you configure that, then you need to be concerned with the Litespeed repository and how large that will get.
Jeffrey Williams
“We are all faced with a series of great opportunities brilliantly disguised as impossible situations.”
― Charles R. Swindoll
How to post questions to get better answers faster
Managing Transaction Logs