Preheat 6 cups vegetable oil to 350 degrees. Whisk together corn meal, sugar, eggs, and milk, set aside. Remove the lobster tail from the shell and skewer the lobster meat through the center from the bottom of the tail to the top. Dip the lobster in the batter and deep-fry until golden brown and crisp, about 4 minutes. Serve with Tamarind Ketchup.
In a large saute pan over medium-high heat, cook all ingredients until tender. Transfer the mixture to the jar of a blender and puree until smooth. Pour the ketchup through a fine sieve into a medium bowl. Season to taste with salt and pepper.