Trim the stems of the artichokes. Rinse lemon and cut it into pieces. Boil salted water and lemon pieces in a large pot. Place the artichokes in boiling water and cook for 40-45 minutes.
Peel the bell pepper with a peeler and cut into quarters, remove seeds and ribs and rinse. Finely dice the bell pepper.
Carve the tomatoes crosswise and blanch for 1 minute in boiling water. Drain the tomatoes, peel, quarter, core and cut into cubes. Peel the shallots and dice. Rinse the chives, shake dry and chop.
Mix the balsamic vinegar with sugar and season with salt and pepper to form a vinaigrette. Toss the bell pepper, tomato cubes, shallots and half of the chives with the vinaigrette.
Lift the artichokes from water with a skimmer. Allow to cool slightly. Pluck the leaves from all the artichokes and remove the hay from bottoms. Distribute the artichoke bottoms and leaves decoratively on plates. Pour the vegetable vinaigrette over and let it pass through.
Loosen the crayfish from the shells. Mix the crème fraîche with lemon juice and sugar, and season with salt and pepper to make a sauce. Mix in the dill.
Mix the crème fraîche into the crayfish and serve on the artichokes. Serve garnished with the remaining chives.