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 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 4 tablespoons of the beet salad; or put the beet salad on a large platter and encircle it with lettuce leaves. Do not use the liquid.