Place the beets on the sheet pan, brush them with oil, and sprinkle with ¼ teaspoon salt and ⅛ teaspoon pepper. Bake for 45 minutes to 1 hour.
In the meantime, combine the cucumber, red pepper, tomatoes, red onion, garlic, remaining salt, and remaining pepper in a large bowl or pot and stir well.
Add the tomato juice, lemon juice, and vinegar.
When the beets are done baking and slightly cooled, peel and discard the skin.
Dice the beets.
Add the beets to the pot with the other ingredients, cover, and chill for 1 hour.