Bring a large pot of salted water to a boil and cook the pasta according to the package instructions for al dente.
Meanwhile, heat the olive oil and butter in a large skillet over medium-high heat. Add the shrimp, lobster and calamari and season with salt and pepper. Sear on each side for 1 to 1 1/2 minutes. Remove to a plate and set aside.
Add the tomato strips, capers, thyme, rosemary, garlic and onion to the skillet and cook for 1 to 2 minutes, stirring often to ensure the vegetables don't brown. Deglaze with the white wine, then add the cream. Bring to a simmer and allow the sauce to simmer and thicken about 4 minutes. Season with salt and pepper.
Add the spinach to the sauce and stir so it begins to wilt. Drain the cooked pasta and add it to the skillet. Add the seafood and any juices on the plate. Add the Parmesan, parsley and lemon zest, turn off the heat and toss everything together until nicely coated in the sauce. Garnish the pasta with more Parmesan, parsley and lemon zest. Serve directly from the skillet.