Preheat the oven to 400 degrees F (200 degrees C).
Combine lemon juice, garlic, Dijon mustard, anchovy paste, salt, and pepper for dressing in a bowl. Stream in olive oil, whisking until well combined; set aside.
Trim off the beets' leafy tops and root ends. Rub each beet with a little olive oil, and season with salt and pepper. Wrap each tightly in a piece of foil and place on a baking sheet.
Bake beets in the preheated oven until you can easily pierce through the centers with a paring knife, 40 to 45 minutes.
Remove beets from oven, and allow to cool still wrapped in foil until you can handle them, 10 to 15 minutes. Rub each beet with a paper towel to remove the skin. Set aside to cool, then cut to your preference, either into chunks or slices.
Tear lettuce leaves into pieces and add to a large bowl along with grapes and red onion. Add beets and give the salad a light stir. Drizzle some of the dressing to your taste, and toss gently until all is well coated. Store any remaining dressing tightly covered in the refrigerator.