Bring a large pot of water to a boil. Add the linguini and cook according to the directions on the box. Drain, reserving 1 cup of the cooking water.
Meanwhile, heat the olive oil in a large skillet over a medium-high flame. Add the garlic and saute for 1 minute. Add the shrimp and cook for 3 to 4 minutes, until the shrimp turn pink. Remove the shrimp from the pan and set aside. Add the lemon juice, white wine, and the reserved cup water to the skillet. Let simmer until the liquid is reduced by about half. Salt and saute the asparagus. Cut into 1-inch pieces. Return the shrimp to the pan and stir in the parsley. Add the drained linguini to the shrimp mixture, tossing to combine. Add asparagus and tomatoes. Season with salt and pepper, to taste.