Hello, @maxgorky,
Thank you for your email!
The Adaptive Images plugin works nicely with Litespeed and its internal cache. This is what our tests have demonstrated.
Also, WordPress cache plugins should not usually interfere with it, because they operate on a different level. At least when the cache plugins do not mess with image delivery. And they usually don’t.
However, CDNs are different thing because they deliver the images themselves and oftentimes do not allow WordPress and the plugin to do anything about it. For this we have developed an experimental mode, called CDN support in the plugin settings page. It is experimental in that it doesn’t always resize all images and some of them are delivered in their original sizes. We are still working on this feature, it is tricky to overcome. You may give it a spin and let us know if and how it works for your setup.
Let me know if I can help any further!
Cheers,
Takis