Peel the asparagus from top to bottom. Cut off the ends generously and then cut the asparagus into bite-sized pieces. Bring the water, salt, sugar and butter to the boil and cook the asparagus pieces in it for about 15 minutes. Remove the pieces with a slotted spoon, drain well and set aside.
Cut the ham into strips. Halve the melons, scrape out the stones and remove the flesh with a ball cutter. Clean, wash and cut the iceberg lettuce into strips. Mix all ingredients together and arrange in the hollowed out melon halves.
Just before serving, mix the ingredients for the sauce, season to taste and drizzle over it.