If you think LSWS does not cache certain page, you need to check the request/response header see if anything prevent the page being cached.
Request with Query String? Request Cookie? Response Cookie? Request cache-control? response cache-control?
If you think a page can be safely cached even with some header can prevent it from being cached, you can adjust the cache policy to force LSWS to cache that page, you may need to create a context for that URL.