In a medium bowl, toss chickpeas with lemon juice and ½ cup of olive oil. Season with salt and pepper.
In a large pot of boiling salted water, cook the broccoli until crisp, about 4 minutes. With a slotted spoon, transfer broccoli to colander and rinse under cold water to stop cooking. Add rigatoni to the boiling water and cook until al dente.
While pasta is cooking, heat the remaining olive oil in a large skillet and add garlic and crushed red pepper. Cook over moderate heat until garlic is golden, about 3 minutes.
Add broccoli and cook until tender, about 5 minutes. Add the chickpea mix and cook until warmed through, about 1 minute.
Drain the pasta and reserve about ¼ cup of the cooking water. Add pasta to broccoli and chickpeas along with the reserved water and season with salt and pepper. Cook over moderate heat, making sure to stir until the rigatoni is evenly coated with sauce. Remove the pan from heat and stir in ½ cup of the Parmesan cheese.
Transfer the pasta to plates and serve, sprinkle with the remaining Parmesan. Serve garnished with thinly sliced lemon rounds, if desired.