You could seek inspiration from our seafood-themed Valentine's Day menu plan!
red wine risotto: 1 cup dry red wine, 1/4 cup port, 1/4 cup unsalted butter, 1 shallot (finely minced), 1/2 cup Arborio rice, 1 1/4 cups chicken stock, 1/4 cup freshly grated parmesan. Warm chicken stock in small saucepan. Reduce wine and port by half. Melt butter, and cook shallot until soft in medium saucepan over medium heat. Add rice and cook, stirring, for 2 minutes. Add the reduced wine mixture and simmer until the liquid is absorbed. Add chicken stock, 1/4 cup at a time, and gently stir until the liquid is absorbed between additions. When rice is al dente (you may only use 1 cup of the stock), stir in parmesan cheese. Serve.
I would also suggest a rice dish. If you do make risotto, try and make sure you spike with some lemon zest, as it will be fat on fat on fat (although that may be your thing). I suggest rice pilaf, its drier, less rich, and if you spike it with some lemon zest, and something like dried cranberries it will cut the fat of the lobster and butter (you are serving it with clarified butter, right?). That's my two cents.
I would not suggest a starch. Instead I would suggest something clean like a groomed or steamed asparagus. My husband disagrees and suggests potatoes au gratin.