unless the backup was created as a self extracting archive its not going to be possible without

• using the litepseed extract utility
• installing litespeed to the target server

Depending on the version of Litespeed that created the backup file you may be able to use the Litespeed recast utility to turn a compressed litespeed backup into a compressed self extracting archive, you will then be able to run this directly on your target server without installing any software, etc.