Heat the olive oil in a medium saucepan over medium heat, add the garlic, and cook for 60 seconds. Add the the zest from 2 lemons, the juice of 2 lemons, 2 teaspoons of salt, and 1 teaspoon of pepper. Bring to a boil, then lower the heat and simmer for 15 to 20 minutes.
Meanwhile, cut the broccoli in florets and discard the stem. Cook the florets in a pot of boiling salted water for 3 to 5 minutes, until tender but still firm. Drain the broccoli and run under cold water to stop the cooking. Set aside.
Bring a large pot of water to a boil, add 1 tablespoon of salt and the pasta, and cook according to the directions on the package, about 12 minutes, stirring occasionally. Drain the pasta in a colander and place it back into the pot. Immediately add the lemon mixture and cook it over medium-low heat for 3 minutes, until most of the sauce has been absorbed in the pasta. Pour the hot pasta into a large bowl, add the arugula,tomatoes, and cooked broccoli. Cut the last lemon in half lengthwise, slice it 1/4-inch thick crosswise, and add it to the pasta. Toss well, season to taste, and serve hot.