Litespeed comes with their own xp procedure to delete litespeed based backup files. Look in the documentation for Litespeed and it will show you how to script it out yourself.

The procedure you'll want to use is: xp_slssqlmaint

The parameters will be in a single string and will be something like:

' -MAINTDEL -DELFOLDER "backup folder" -DELEXTENSION "backup extension here"'

-DELUNIT "unit number - eg 60" -DELUNITTYPE "minutes" -DELUSEAGE';

You can delete files based upon days, hours, minutes, etc...