Changing between Apache vs. Litespeed vs. OpenLitespeed will not have much affect on immediate performance, as the bigger concern is optimizing your configuration (settings) rather than just swapping servers.
That said, if you are running a high-traffic WooCommerce site than there might be a lot of uncached dynamic queries (esp. on your checkout and cart pages) going on meaning your database performance and RAM are important here, try:
MySQL + object cache (e.g. Redis) + plenty of RAM memory for Redis to use (seriously high traffic sites might consider a dedicated/managed remote database server)
Besides that, stop using janky WordPress cache plugins like WP Super Cache or WP Rocket and use actual server-level caching instead, like the pros do. Those plugins are fine on low-traffic sites that want an easy way to manage caching, but not for high-traffic.
This is why Nginx is so easy for standalone high-traffic sites like this, because you simply setup a LEMP stack server using open source software and FastCGI Cache is included in Nginx already. Free scripts like my own project SlickStack can do the entire setup for you in less than a few minutes (there are several others too, like EasyEngine, Webinoly, WordOps, CentminMod, and more).
Of course, Litespeed has server-level caching too called LSCACHE and Apache has multiple cache features as well, but there are no easy installation scripts for these that I'm aware of meaning that you will need to know exactly how to configure the OS, server, caches, etc, or you will simply need to continue using shared hosting companies that do all that configuration for you (e.g. cPanel).
TLDR both Litespeed and Apache are a better fit for shared hosting companies using e.g. cPanel than for standalone sites looking for cleaner config and faster speed/security. So if you really want to stay using Apache or Litespeed why not just keep using your shared hosting company instead, and ask to upgrade to a better plan or whatever.
As far as "reading that Litespeed is faster" see my answer here, where I briefly warn users that Litespeed has been posting propaganda: