@w3com first, my apologies for this late reply! Asset CleanUp does work together with LSCache and Autoptimize, however, there are things you need to be careful with if you’re using three performance plugins.
Make sure not to mix features (e.g. if you enable minify CSS in LSCache, don’t do the same in Autoptimize and Asset CleanUp as you will use more resources and having all these features enabled might confuse you as they will be difficult to manage, by going through so many options overall) and be careful when using Minify HTML in Autoptimize/LSCache as there were some issues with Asset CleanUp in terms of options not working when the HTML was altered.
This is currently under testing and I’ll make sure that in a future version of the plugin, there will be a few compatibility fixes added. I’ll make sure the authors of LSCache and Autoptimize will be contacted in case they might need to do some changes on their end to make sure all three plugins will work smoothly.
Finally, think if you really need to use three plugins for a faster page load. Some just use one and a good hosting that has its own caching system. The more plugins you use, the more difficult to maintain settings will be, so you’ll need to think about this too.