Place first 9 ingredients in a medium bowl; toss gently to combine. Remove 3 hearts of palm from jar; reserve remaining hearts of palm for another use. Dice 1 heart of palm; add to tomato mixture. Cover and chill at least 2 hours.
Cut remaining 2 hearts of palm in half lengthwise. Arrange 2 hearts of palm halves, 3/4 cup lettuce, and 3/4 cup tomato mixture on each of 2 salad plates. Top each serving with 1/2 teaspoon cheese.