Thaw lobster tails, if frozen. In a large saucepan, cook lobster tails, uncovered, in enough salted boiling water to cover for 7 to 8 minutes or until shells turn bright red and meat is just tender; drain. To stop the cooking process, hold under cold running tap water. When cool enough to handle, remove and discard shells. Coarsely chop meat (you should have about 1-1/2 cups). Cover; chill in the refrigerator until ready to use.
In a large mixing bowl, combine the tomatoes, cucumber, sweet pepper, vegetable juice, green onions, vinegar, cilantro, basil, olive oil, garlic, and cumin. Gently fold the lobster into the tomato mixture. Cover and chill for 4 to 8 hours to allow flavors to blend.
To serve, ladle into chilled serving bowls. If you like, garnish with basil sprigs. Makes 6 appetizer servings.