Bring a large pot of water to a boil. If using fresh lobster tails, add 5 lobster tails to boiling water and cook 6 minutes. Using tongs, transfer tails to a bowl and let cool.
Season boiling lobster water heavily with salt and add 1 pound bucatini; cook until al dente according to package directions. Drain, reserving 1 cup pasta water. Wipe out pot and return to stove top.
Remove and discard husks and silk from 3 ears of corn. Cut off kernels (should get about 2 cups). Using back of a chefs knife, scrape cobs to collect the little sweet bits of kernel and “milk” (this should yield about 3 tablespoons); reserve. Discard cobs.
Melt 2 tablespoons butter over medium-low heat in a now-empty pot. Add 2 cloves sliced garlic and ½ teaspoon red pepper flakes; cook until fragrant, about 1 minute. Stir in corn (and scraped bits) and reduce heat to low. Cook until corn is sweet and soft but not browned, about 8–10 minutes.
Once lobster is cool enough to handle, crack open shell and remove meat; you should get at least 8 ounces lobster meat. Dice the lobster meat.
Add lobster, 1 ½ cups halved cherry tomatoes, cooked pasta, 8 ounce crème fraîche and ½ cup pasta water; toss to coat. Increase heat to medium and cook until sauce is slightly thickened; season to taste with salt and pepper, adding a touch more pasta water if necessary to coat noodles. Remove from heat and fold in ½ cup Parmesan and ⅓ cup torn basil leaves.
Spoon into pasta bowls and top with remaining Parmesan, more fresh basil and cracked black pepper.