For the artichokes, cut off the stems under the leaf base and then the upper third of the leaves. Wash the artichokes well under running water.
In a large pot, boil the lemon slices, salt and sugar with water. Add the artichokes and cook for about 35 minutes, depending on the size.
Remove and drain. (Cut larger ones in half and remove the "hay").
Saute olive oil, balsamic vinegar and tomato cubes with chopped olives in a pan, season with salt and pepper and add to the artichokes.
A dip with sour cream and garlic also goes well with a dip of the leaves.