Cook the pasta according to the package instructions. Reserve ½ cup of pasta water, then drain.
Meanwhile, sauté the shrimp in a large skillet until pink and cooked through, about 2–3 minutes per side.
Stir in the lemon pesto, lemon juice and a splash of reserved pasta water.
Add the cooked pasta and arugula, tossing until everything is coated and the arugula is just wilted. Serve immediately.