Bring a large pot of salted water to a boil. Add the lobster tails and cook until they begin to curl, 5 to 7 minutes. Using tongs, remove the lobster tails and set aside until cool enough to handle. Add the pasta to the boiling water and cook, stirring occasionally, until tender but still firm to the bite, 10 to 12 minutes. Drain and place in a large serving bowl.
Using kitchen scissors or a heavy knife, cut along the underside of the lobster tails and remove the meat. Chop the meat into 3/4-inch chunks. Set aside.
In a large nonstick skillet, cook the bacon over medium-high heat until brown and crispy, about 10 minutes. Remove the bacon and drain on paper towels.
In the same skillet, add the garlic and cook until aromatic, about 30 seconds. Add the tomatoes (and juices), clam juice, cream, 1/2 cup basil, 2 teaspoons salt and 1/2 teaspoon pepper. Bring to a boil and scrape up the browned bits from the bottom of the pan with a wooden spoon. Reduce the heat to medium and simmer until slightly thickened, about 5 minutes.
Add the shrimp and cook, stirring occasionally, until just cooked through, about 3 minutes. Add the lobster and bacon. Simmer until warmed through, 1 to 2 minutes.
Pour the tomato mixture over the cooked pasta and toss until coated. Garnish with the remaining 1/2 cup basil and season with salt and pepper.