Bring a large pot of salted water to a boil. Cook the pasta to al dente, according to the package instructions. Reserve 1 cup of the pasta water.
Meanwhile, melt the butter in a large saute pan over medium heat, stirring occasionally. Let the butter cook until it turns light brown and smells nutty, 3 to 5 minutes. Stir in the chile flakes. Lower the heat, add the miso paste, and whisk until fully incorporated into the butter. Add 1/4 cup of the reserved pasta water. Toss in the shrimp and saute until cooked through and pink, 2 to 3 minutes. Turn the heat to low.
Drain the pasta and add it to the saute pan. Add another tablespoon or more of pasta water, if needed. Toss in the lobster, parsley and 1/2 teaspoon salt and pepper, and gently toss until the pasta is coated with miso sauce and the lobster is warm, about 2 minutes. Serve immediately.