Bring a pot of salted water to a boil. Cook the pasta according to the package directions, adding the broccoli for the last 3 minutes. Scoop out ½ cup of the cooking water, then drain.
While the pasta cooks, heat the oil in a large skillet over medium-high heat. Season the shrimp with the salt and pepper and cook for 1–2 minutes per side, until pink and opaque.
Add the garlic and cook for 30 seconds.
Reduce the heat to low. Add the pasta, broccoli, butter and ¼ cup of the cooking water. Toss until the butter melts.
Add the Parmesan and lemon juice and toss until the sauce coats the pasta, adding more cooking water if needed. Serve right away.