When configuring LiteSpeed for SQL Server, an estimate of repository database storage may be required.

LiteSpeed repositories collect and retain statistics on backup activity that occurs through LiteSpeed, including backups conducted from the LiteSpeed UI Console, command-line, or using the extended stored procedures. Repositories collect and present statistics for registered servers. 

How much does the repository grow when a backup is made?

Each backup writes a row to the LiteSpeedLocal database and that is updated tp the LiteSpeedCentral database

Benchmark for growth of the LiteSpeed repositories (both the LiteSpeedLocal and LiteSpeedCentral). This is an average growth value computed from the number of tests made on different SQL Servers.

For 100 backups repository growth is about 360 - 400 KB

NOTE: Test have been made on 200 backups. Results show about 750 - 800KB growth.
.Additional InformationIts hard to operate by every backup operation because it increases the repository differently (from no change to 12KB) but in average it is ~400KB per 100 backups.

There are tools in LiteSpeed to manage the volume of data (from the Help file):
LiteSpeed_DeleteActivity
This stored procedure removes LiteSpeed activity and information about LiteSpeed backups based on the date and time specified. Additionally, if appropriate parameters are specified, it removes log shipping history, jobs and maintenance plans history, DST status, and information about deleted databases.

-or-

The task in the Maintenance Plan - Clean Up History
Remove historical data from the msdb database and LiteSpeed Local and Central repositories for the following:

o    Back up and restore history

o    SQL Server Agent jobs

o    Maintenance plans

o    LiteSpeed activity

Note: LiteSpeed activity is removed from the Central repository, only if it is located on the same server, where the Local repository resides.

o    Any information for deleted databases

o    Log shipping history

o    Status history (Job, DTS, Maint Plans)