Put an ounce of butter into a medium-sized sauté pan with a drizzle of olive oil over medium heat. Add the shallots and cook until translucent, about 3-4 minutes. Then, add the lemon juice and white wine, stirring everything together. Add the thyme, salt, and pepper and stir slowly again. Then, add the rest of the butter slowly, letting each piece melt into the sauce completely. Turn the heat down slightly and let the sauce reduce.
Meanwhile, bring a pot of salted water to a boil. Cook the linguine for 7–11 minutes, until al dente. Strain the linguine and add immediately to the white wine sauce, followed quickly by the cooked lobster meat. Stir everything together, making sure it’s all coated and incorporated. Plate immediately and garnish with Parmesan cheese.