Cook whole beets in plenty of water. Depending on the age of beets, it will take anywhere from 30 minutes to 1 hour.
When beets are tender, drain and peel them and cut them into julienne strips. Mix together vinegar, sugar, salt, mustard, caraway seeds and horseradish. Adjust the sugar and salt to your own taste. Marinate beets in the dressing overnight.
When ready to serve, form cups out of the lettuce leaves and fill them with 3 or 4tablespoons of the beet salad; or put the beet salad on a large platter and encircle it with lettuce leaves. Do not use the liquid.
For a very elegant service, use small heads of Boston-type lettuce; remove centers and fill heads with beet salad. Serve one to a person. It isn’t exactly the cost of Trimalchio’s feast, but for 4 persons you will need 4heads of lettuce.