Preheat the oven at 400 F. Line a baking sheet with aluminum foil.
Place the trimmed asparagus and lemon slices on the baking sheet, toss with 1 tbsp of oil, salt and pepper.
Bake for 20 minutes. Cut the asparagus into 1-2 inch pieces once they cooked and cooled down.
As asparagus is getting bake, cook the pasta as per the package instruction. Add generous amount of salt to the pasta water and cook the pasta al dante (firm to bite).
In a large skillet, heat 2 tbsp of olive oil on a medium heat.
Once hot, add minced garlic and cook until it turns light brown.
Next, stir in the flour. Cook for half a minute and start pouring milk, 1/2 cup at a time and whisking in parallel.
Once all milk is added, reduce the heat to low and keep stirring until the sauce thickens.
Add juice of one lemon, salt, pepper as per taste and roasted asparagus pieces (leave about 1/4th of asparagus to serve on top). Give a nice stir.
Add cooked pasta and toss to coat.
Serve warm, topped with remaining asparagus and freshly grated parmesan cheese.