Using a mandoline or sharp chef’s knife slice fennel into paper thin strips. Roughly chop raddichio. Toss with olive, lemon and season with salt & pepper to taste.
Prepare the lobster tails by patting them dry and laying them flat on a cutting board. Using a sharp knife and starting from the flippers, cut through the shell all the way along the top. Peel off the whole shell. Heat the butter of ghee in medium sauté pan. Sear the lobster meat for about 6 minutes, turning frequently. Remove lobster from pan and toss with fennel radicchio salad. Serve immediately.