Bring a pot of water to a boil and cook the beetroots 25 minutes, or until tender. Cool, peel and cut into 1cm slices. Place slices in a bowl with the balsamic vinegar and marinate 15 minutes.
Place a few beetroot slices in a microwave-safe dish, reserving vinegar. Sprinkle each slice with some of the reserved vinegar, lemon juice, feta cheese and walnuts. Top with more beetroot slices, and sprinkle again with vinegar, lemon juice, feta and walnuts. Repeat, building the stacks as high as you like.
Place stacks in the microwave, and cook 40 to 60 seconds on Medium. Cool slightly before serving.