Pagespeed doesn't check the speed of a page. It checks how long it takes to display after all data has been loaded from the server, so the name "Pagesspeed" is wrong and should be renamed to "Display Speed". Pagespeed Insights doesn't honour if you use a HTTP cache or not.
If you have the Smarty cache in PrestaShop enabled this costs more load, but only if a page isn't cached. If it is cached the Smarty cache is out of order, so it doesn't make sense to use PrestaShop Smarty cache function with LScache. Disable it.