Combine the first 7 ingredients in a bowl. Cover dressing and refrigerate until needed. Preheat grill to medium-high. Brush the cut side of each half lobster tail with 1 Tbsp. of oil; season with salt and pepper.
Lightly oil your grill. Grill the lobster, cut side down, 2 minutes. Turn lobster cut side up and grill 2 minutes more, until cooked. Cool lobster a few minutes, then pull out the meat, cut into pieces, and set aside.
Brush steak with the remaining oil, season with salt and pepper, and grill to desired doneness, allowing 3 to 4 minutes per side for rare to medium-rare. Transfer steak to a cutting board, rest 5 minutes, and then remove the bone and cut the meat into thin slices.
Divide the lettuce among 4 plates and top lettuce with the lobster, steak, avocado, tomato and cucumber. Drizzle each salad with dressing and serve.