Prepare the flavor base; melt butter in a large stock pot over medium-high heat.
Add chopped onion, celery, carrots, and tomatoes. Cook, stirring for 5 minutes.
Add the lobster meat and cook for 2-3 minutes.
Sprinkle the flour over the veggies and lobster and stir until it's all coated nicely. Cook the flour for 1 minute.
Add the liquid:
Add the liquid; pour the milk, heavy cream, and chicken or lobster stock into a saucepan, while whisking constantly.
Season the bisque with Old Bay seasoning, salt and pepper, to taste.
Reduce the heat and simmer the bisque until slightly reduced.
Finishing touch:
At this point, you can blend the bisque with an immersion blender or strain the bisque through a fine mesh, pressing down the solids.
Adjust the seasoning and serve the bisque warm.
Notes
If you have fresh lobster, you can use it. Here is how to prepare lobster tails: add 4 lobster tails to a saucepan with two stalks of celery, 1 halved onion, 4 peppercorns, 2-3 thyme sprigs and enough water to cover all. Simmer the stock for 20-30 minutes. Strain the stock and remove the lobster meat from the tail.