Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
Melt the butter in a skillet over medium heat. Whisk in the flour and cook on low heat for 10 minutes.
In a separate saucepan over low heat, warm the milk. Turn off the heat and whisk the milk into the flour and butter mixture until fully incorporated. Return the heat to medium and bring to a simmer, whisking constantly. Continue to simmer (not boil) for 15 minutes, whisking occasionally. Season with salt.
Whisk in the stock, both cheeses and salt and pepper.
Stir the cheese sauce into the pasta to coat. Add the lobster meat.
Transfer the pasta to a baking dish, top with breadcrumbs and more cheddar cheese, and broil for 2-5 minutes, until melted and golden on top. Watch carefully to avoid burning
Place all vinaigrette ingredients other than the oil in a blender. Purée until smooth. With the motor running, drizzle in the oil until emulsified. Season to taste.
Combine the lettuce and tomatoes in a large bowl and toss with lemon shallot vinaigrette.