I had major issues with delay of the firsts https request on my site which is on a pretty good shared server. I optimized it in all possible ways through the back-end. I put the site on Cloudflare, added custom mod_headers.c, optimized the db tables... Even if that helped, specially the db optimization, I was still not happy as before and even to some extend after I was getting a 10-20 seconds of TTFB delay (waiting time) from the request to server. As I saw there was nothing more I could do, I thought about getting a HTML caching module from PrestaShop, but was recommended by TMDhosting to try the Litespeed module. As it was free and communicates directly with your installation of LiteSpeed Web Server, I wanted to get that one before considering a 3rd party module. Thanks, I'm happy now my site is fully loaded within 2-3 seconds. Please keep the support rolling for PrestaShop!