Scrub the beets very well. Fill a 3-quart saucepan halfway with water and bring to a boil. Cook the beets until tender when pierced with a sharp knife, about 45 to 60 minutes. Drain well and let cool. Slip the skins off the beets. Dice the beets and place in a bowl.
To make the dressing: whisk together the lemon juice, garlic, salt, pepper, and oil. Pour a few tablespoons of the dressing on the beets and toss.
Just before serving, combine the greens, arugula, and scallion in a large bowl. Pour on most of the remaining dressing and toss. Add more if needed.
Place the greens on 4 salad plates. Spoon on a mound of beets. Sprinkle with goat cheese and walnuts. Serve immediately.