Preheat a grill to medium high. Bring a large pot of salted water to a boil. Combine 1/4 cup olive oil, the garlic, lemon zest, red pepper flakes and 1/2 teaspoon salt in a large bowl; set aside.
Toss the broccoli rabe with the remaining 2 tablespoons olive oil and a big pinch of salt; spread out in a grill basket. Transfer to the grill along with the sausages. Cook, turning occasionally, until both are well marked and the sausages are cooked through, 8 to 10 minutes. Transfer to a platter.
Add the pasta to the boiling water and cook as the label directs for al dente. Meanwhile, roughly chop the broccoli rabe. Halve the sausages lengthwise and cut crosswise into 1/2-inch pieces. Cover and keep warm.
Reserve 1/2 cup cooking water, then drain the pasta and add to the bowl with the garlic oil. Add the broccoli rabe, sausages and 1/4 cup of the reserved cooking water; toss well to coat. If the pasta is too dry, add more cooking water, 1 tablespoon at a time. Season with salt. Divide among bowls and top with the oregano and parmesan.