Prepare the béchamel: Make a roux with butter and flour, then add milk, nutmeg, thyme, and salt. Bring to a boil and let it thicken.
Cook the asparagus: Cut the asparagus into pieces and cook them in a pan with olive oil and salt for 10 minutes, adding the stems first and then the tips.
Assemble the lasagna: Layer the béchamel sauce on the bottom, followed by lasagna sheets, more béchamel, asparagus, mozzarella, and grated cheese. Repeat layers until all ingredients are used.
Bake the lasagna: Cook in a static oven at 180 degrees Celsius for 20 minutes, then grill for the last 5 minutes at 200 degrees Celsius.