Sorry for the delayed response. Been lots of travel for me recently.
CS-Cart can certainly be used with LSCache, but, yes, you will see some of the issues that you have with Magento. We don't currently have a template for using LSCache with CS-Cart. And, unfortunately, I don't anticipate one soon, either. If you do develop a set of configurations that works well with CS-Cart, please share it with the community.
Cheers,
Michael