There are two elements: LiteSpeed Web Server (LSWS) and LiteSpeed Cache for WordPress (LSCWP). LSWS runs on the server as a drop-in replacement for Apache. LSCWP is the caching plugin for WP. But they also do cache plugins for Magento, Joomla, OpenCart and other platforms.
Best results are obtained when the web component and the cache plugin are used together but the plugin can be used on its own.
If you look at most hosting companies, they offer various managed WordPress hosting packages, some based on Litespeed, others on Nginx. All make good use of caching. But it’s the fact that they’re managed that is significant.
Here’s a couple of examples:
The ones that are using Litespeed in their managed packages also use the caching plugin. But it is difficult (if not impossible) to persuade hosting companies to support ClassicPress if a key component of the underlying technology doesn’t support it.
So if we can get Litespeed to commit to supporting CP, the theory is that it will make it a lot easier to get hosting companies to support it too and perhaps offer a dedicated, managed ClassicPress hosting package.
And yes, it has been mentioned that Litespeed isn’t essential for ClassicPress sites, but that is missing the point.
Obviously everyone will have different experiences. When I tested LSCWP in conjunction with LSWS, it made a noticeable difference to most of my sites, particularly the larger ones.