In a pot of boiling, salted water, cook the pasta until al dente; drain, reserving 1/3 cup of the cooking water.
Meanwhile, in a large skillet, heat 2 tablespoons olive oil over high heat. Working in 2 batches, add the squash and cook, turning occasionally, until browned, about 5 minutes. Transfer to a large bowl; stir in the lemon juice.
Lower the heat to medium-high; add the remaining 1 tablespoon olive oil to the skillet. Add the onion and cook, stirring, until softened, about 3 minutes. Stir in the garlic, lemon peel and reserved pasta cooking water.
Add the pasta to the squash mixture. Toss in the mint and cheese; season with salt and pepper.