Steam asparagus in water for 5 minutes or until crisp-tender.
Lay one sheet of phyllo dough in a cooking spray coated 13 by 9-inch baking dish, cut if needed to fit. Spray dough with cooking spray. Layer nine more sheets of phyllo on top in same manner. Layer spinach, feta, and asparagus on top of dough and cover with the rest of the phyllo in the same manner as above. Slice into 12 pieces and bake at 350 degrees F for 30 to 35 minutes or until crispy.
Melt butter in a pot; whisk in flour and milk. Add in lemon juice, dill, thyme, and salt and let boil 1 to 2 minutes or until thick. Serve sauce over spanakopita.