Place the lychees in a food processor and puree until very smooth. Add the brewed black tea, lime juice and lime zest and pulse a few times to incorporate well. Transfer the mixture to a 10 by 10-inch pan. Freeze overnight.
Using the bottom of a fork, scrape the granite into the hollowed out limes. Scrape a small amount of the granite onto the centers of the plates and top with the filled limes (2 halves per plate).