Combine onion, vinegar, 1/4 cup water, sugar and 1/4 teaspoon salt in a saucepan over high heat; bring to a simmer. Cook 1 minute; remove from heat; and let cool until ready to use.
Bring a medium pot of salted water to a boil. Add lobster tails and cook for 6 minutes. Remove from water and let cool. Once cool enough to handle, lay them flat on a cutting board. Using a sharp knife and starting from the flippers, cut each in half lengthwise. Pull out the meat, roughly chop and set aside.
Heat your tortillas in a pan or in the oven, then wrap in a clean dish towel to keep warm.
Melt butter in a small sauté pan over low heat. Add garlic and cook for 2 minutes. Whisk in lime juice and remove from heat. Toss lobster meat and cilantro in the pan to warm and season with salt. Divide lobster between tortillas. Top with pickled onion, grated carrots and avocado. Serve warm.
Note: Don’t throw away the cooking water or the lobster shells. You can put the shells back in the water and boil to make a delicious lobster stock. Use stock for soups or to make a lobster risotto.