form key value is unique per customer. We need to punch a hole for any place that reference the formkey. So the cached page is generic and can be shared by everyone. Server will just replace the real form key when serving to individual user. when magento output, it should replace litemage formkey with esi:include tags.
Do you have any plugin that will do html minify? It may delete those esi:include tags. You can try to enable "Use alternate ESI syntax" and see if it shows up. esi:include will be processed internally by lsws, so to end users, you will not see this and only see the real form key.