Cook the noodles according to the package directions.
Meanwhile, break off the tough ends of the asparagus and cut the spears into 1-inch pieces.
When the noodles go into the boiling water, heat the oil and butter in a large heavy skillet over medium heat.
When the butter is melted, stir in the garlic then immediately add the asparagus, stirring to coat it.
Sauté the asparagus, stirring occasionally, for about 4 minutes until it is tender-crisp.
Stir in the spinach and lemon juice, cover, and steam it for about 2 minutes, then uncover it and cook it, stirring frequently, for about 2 more minutes until the spinach is completely wilted. Season the vegetables with salt and pepper.
Drain the noodles, combine them with the asparagus and spinach, and stir in the Parmesan cheese until it melts. Serve it immediately or refrigerate it for up to 2 days.