Supreme the oranges by cutting off the top and bottom ends, removing the rind with a sharp knife, and slicing between the segments to release the supremes.
Drain and pat the hearts of palm dry, then slice them into ½-inch rounds.
In a large mixing bowl, combine the arugula, cucumber, radishes, shallots, and hearts of palm, tossing gently.
Drizzle the lemon vinaigrette over the salad and toss gently to coat.
Plate the salad, arranging sliced avocado on top and sprinkling with parmesan cheese.