For Virtualmin is no plugin available, so you must do a Generic LSWS Web Server Installation, but be carefull. It is not tested:
https://www.litespeedtech.com/support/wiki/doku.php/litespeed_wiki:installation:generic
Of Course there is a way, but any other way brings new issues. The consequence of this dilemma could be to disable cache for any users that doesn't accept cookies.
RewriteCond %{HTTP_COOKIE} !name_of_vary_cookie [NC]
RewriteRule .* - [E=Cache-Control:no-cache]
Not lscache uses cookies, your plugin uses vary cookie. Using cookie to store information which device is used is a absolute wrong method. To me, bad idea to use cookie for this. Ask LiteSpeed staff if they re-design this plugin.
Strange.... Have already asked support of PHP framework? You know that you can set such settings also in cPanel for each account?
btw. you can disable zlib.output_compression. Set compression in LSWS WebAdmin to get zip AND brotli compression instead.
It seems you need a more powerful hosting. If pages are cached speed is okay, but if not cached your shop needs more than your server is able. You need at least a VPS with SSD hardisk.
Check your settings. Disable recompile template files if enabled, maybe that helps.