Please try to move the litespeed rewrite section to the top of the .htaccess file, graceful restart the web server, and check the cache again. Let us know if it works.
There seems to be a misconfiguration of lscache as there is no x-litespeed-cache header. Screenshot image taken from lsws forum. Also
x-turbo-charged-by: LiteSpeed header is missing if CloudFlare is used.
Please try to move the litespeed rewrite section to the top of the .htaccess file, graceful restart the web server, and check the cache again. Let us know if it works.