Combine the first 4 ingredients in a small bowl; stir well.
Combine 3 tablespoons juice mixture, mango, onion, chile, and mint in a bowl, and stir well. Set mango mixture aside.
Separate endive into leaves, reserving 12 outer leaves. Thinly slice the remaining leaves; set aside.
Remove meat from lobster tails and claws; set claw meat aside. Thinly slice tail meat; set aside.
Drizzle 1/3 cup juice mixture over the salad greens, and toss gently to coat. Divide greens evenly among 4 salad plates. Arrange 3 endive leaves, 8 jicama strips, and 6 asparagus spears on 1 side of each plate. Arrange claw meat on other side of each plate. Spoon 1/2 cup mango mixture in center of each plate. Arrange tail slices, overlapping, on top of mango mixture. Drizzle remaining juice mixture evenly over lobster meat. Sprinkle pepper over salads, and garnish with sliced endive.