Dice half of the lobster into 1⁄2-inch pieces. Slice the other half into nice pieces for the top of the stack. Place in separate bowls.
In a small bowl, mix together the mayonnaise, lemon juice, mustard, 1 tablespoon red onion, Tabasco, and salt. Toss with diced lobster pieces and set aside.
In a medium bowl, toss the mango, bell pepper, and jalapeno together and set aside.
In a small bowl, toss the avocado, red onion, and lime juice together. Season with salt and pepper and set aside.
Divide the avocado mixture between 4-3 inch round ring molds or biscuit cutters and gently press together. Top with mango mixture and gently press into the ring. Spoon the diced lobster mixture onto the mango and gently press to hold its shape.
Arrange several pieces of sliced lobster to the top of the stack. Unmold on the plate you wish to serve the salad on.
Garnish with fresh basil and basil oil, if desired.
Spoon avocado mixture into the bottom of a martini glass about 1-inch deep. Spoon a layer of mango mixture over the avocado. Add the diced lobster over the mango mixture and top with several lobster slices. Repeat for a total of 8 cocktails.