Every hosting server we run serves pages with LiteSpeed rather than Apache. The reason is specific rather than magical, and it is worth understanding before you believe anybody's benchmark, including ours.
The mechanical difference
The part that matters for a PHP site is how the web server talks to PHP. In a common Apache setup a PHP process is started to handle a request and finished afterwards. LiteSpeed keeps a process alive and reuses it, which removes the start-up from every request. On a site where a page is assembled from a database on each view, that is the largest single saving available without changing the site itself.
The second part is static files. Images, stylesheets and scripts are served directly rather than handed to another layer, so a page with forty assets spends less time on the thirty-nine that are not the HTML.
What it does not fix
A theme that loads nine hundred kilobytes of JavaScript is slow on any web server. A plugin that runs forty database queries to draw a sidebar runs them whatever is in front of PHP. A site with no caching asks for the same work on every view. No web server fixes any of those, and anybody telling you otherwise is selling the server rather than explaining it.
This is why we do not publish a multiplier. The honest statement is that the server removes one class of overhead and leaves the rest of your site exactly as it is.
Compatibility
LiteSpeed reads Apache's own configuration directives, so a .htaccess file written for Apache works unchanged. Rewrite rules, redirects, directory protection and the rest behave as you expect. Moving a site from an Apache host to one of our accounts does not mean rewriting your configuration.
On WordPress specifically
LiteSpeed Cache is a WordPress plugin that talks to the server directly, so a page can be served from cache without PHP running at all. It is a plugin you install, not something that happens by itself, and on a site that was already caching well the difference is smaller than on one that was not.
Every WEB-HOST, WP-HOST and Business plan runs on LiteSpeed. There is no faster tier to upgrade into, which is the way we would rather sell it than as a feature of the expensive plan.