Bring water to a boil in a large 3 quart pot. Salt generously.
Season shrimp with salt and pepper.
Add one tablespoon of olive oil and one tablespoon of butter to a large skillet over medium-high heat.
Add shrimp and sauté for about 2 minutes. Flip shrimp over and continue cooking until shrimp are pink and no longer translucent, about one minute longer. Remove shrimp from skillet.
Add remaining tablespoon of olive oil and tablespoon of butter to the skillet.
Add asparagus and lemon juice and toss to combine.
Sauté for 3 to 5 minutes or until asparagus are crisp-tender and bright green in color.
At the same time you are sautéing the asparagus, add the gnocchi to the pot of boiling water and cook according to package directions, about 2 minutes. Remove gnocchi with a slotted spoon.
Add gnocchi and shrimp to the skillet with the asparagus. Top with pesto and gently stir to combine.
Top with Parmesan cheese and serve immediately.