Cook linguine according to package directions, omitting salt if desired. Drain and transfer to serving bowl.
Heat 2 teaspoons of oil in a large non-stick skillet over medium-high heat. Add shrimp and cook just until opaque in the center. (1-1/2 to 2 minutes per side)Transfer to a plate.
Heat 1 teaspoon of the oil in the same pan and add the lobster pieces, stirring frequently until just heated through. Transfer to the plate with the shrimp.
Heat remaining 1 teaspoon of oil in the skillet over medium heat. Add the garlic, thyme and crushed red pepper. Cook, stirring constantly until fragrant, about 30 seconds. Stir in the tomatoes and tomato paste and cook until slightly thickened.
Return shrimp and lobster to the skillet and cook stirring frequently tunil heated through.