No airline has a lounge pre-security. There are two a pre-security lounges the Consular lounge (only for traveling foreign diplomats, government officials, dignitaries and other official guests and VIPs) and Military Hospitality Lounge. No airline lounge program can get you into any of those. Here is the link to VIP lounges at MIA http://www.miami-airport.com/vip_clubs_and_lounges.asp
If you have 3 hours to kill that will give you plenty of time to clear security, go to lounge and then back to your concourse. Almost positive you can do that, but check with the airport just in case. With all the ever changing security measures, I can't assure you what you can and can't do around any airport anymore. Have fun in NY!!