Cut the melon into halves. Cut crosswise into thin slices. Cut off the outside skin. Cut the beef into thin slices. Grill or broil the beef to desired doneness. Arrange the lettuce on a large salad platter. Top with the grilled beef, melon slices, and cucumber sticks. Spoon the sauce over the top.
Cut the melon into halves lengthwise. Use a grapefruit knife or small sharp knife to scoop out the pulp. Combine the melon pulp, lime juice, green onion, oil, cumin and garlic in a blender or food processor container. Cover and process until well blended.