Preheat the oven to 400F.
Bring about 6 quarts of water to a boil and add about 2 tablespoons salt (optional). Prepare a bowl of ice water.
Trim the asparagus and boil for 1 minute. Use tongs to remove the asparagus from the hot water; reserve asparagus cooking water. Refresh asparagus in the ice bath for 30 seconds. Use tongs to transfer the asparagus to a colander, drain well, and cut each spear in half crosswise and set aside.
Heat olive oil over medium heat in a 12 to 14 inch saut pan.
Add the eggplant and cook until golden brown and soft, about 5 minutes. Drain on a paper towel and set aside.
Cook the Lasagne sheets in the same boiling water as the asparagus and cook for 2 minutes less than the package instructions. Drain and separate.
Prepare a 13x9 baking pan by coating with butter or cooking spray.
Layer 4 sheets of lasagne on the bottom of the pan; top with 6 pieces of asparagus, 3 to 4 slices of eggplant and 3 tablespoons of besciamella sauce.
Top with 4 sheets of lasagne, asparagus and eggplant as above, and 3 tablespoons of pesto sauce.
Repeat these 2 layers for a total of 4 layers. End with 4 sheets of lasagne, remaining besciamella sauce and grated cheese. Sprinkle with bread crumbs.
Place the baking pan on a baking sheet and bake for 20 to 25minutes, or until bubbling and golden brown on top.