I test all the possibles parameters for gzip compression (Auto Update Static and others) and I never got gzip for html static files when lsws has no write permission in the directory the file is... Is it normal ?
(In the same directory, gzip work only for dynamic files)
LiteSpeed needs write permission to create a copy of the compressed static file under the same directory. If you prefer not to give write permission to the server process, you can create them manually, just rename "*.gz" file to "*.lsz".