Yes, but if a function is disabled, then it is disabled. There is no cache header: x-litespeed-cache: cache is off, but there is a x-litespeed-cache: no-cache header that occurs if a page is either manually excluded from being cached or by its type, but only if cache is not disabled.
when you first check by pagespeed, you can see in OPPORTUNITIES "Reduce server response"- this is still NO lscache, after second check "Reduce server response" disappear - this is already generated lscache (for this page only).
for different User Agents/devices must be generated it's own cache.
this is work for crawler (recache, cache warmer)