Chop cooked lobster meat into chunks. Break up any clumps of fine shredded meat. Drain well, squeezing any extra liquid from meat.
While sauce is thickening, cook pasta in salted water until el dente. Drain well.
Prepare white sauce by combining flour and butter over medium low heat, cooking until foamy and well incorporated.
Heat milk in microwave until warm, do not boil. Add a small amount to pot, whisk until combined, then add remaining milk. Cook slowly over medium low heat, whisking until sauce is thick, smooth and uniform in colour.
Remove from heat and stir in cheeses. Season with salt and pepper. Taste and adjust seasoning accordingly.
Add lobster meat to sauce and stir to combine. When pasta is cooked and well drained, add to sauce mixture. Pour into an oven safe small to medium sized baking dish, approximately 9 inch oblong or 8 inch round.
Prepare topping by melting butter, then adding remaining ingredients. Mix well and sprinkle evenly over top of dish.
Bake on the centre rack of a preheated oven at 350° for about 30 minutes, until top is browning and edges are bubbling. If you are baking later from a cold dish, increase cooking time by about 10 minutes.