Melt the butter in a large skillet over medium heat. Add the shallot and fennel and sweat until tender, about 3-4 minutes. Add the lobster meat, salt and pepper and continue cooking for 3-4 minutes, stirring frequently. Deglaze the pan with the wine and cook until about half the wine has evaporated, about 2 minutes. Add the stock and bring to a simmer. Fold in the cooked risotto and stir frequently until stock has been absorbed and the risotto is hot.
Divide among 6-8 bowls and finish each with 1 tsp chopped chive, shredded cheese and extra virgin olive oil as needed.