In a gallon-sized resealable bag, add the olive oil and the juice only from the 3 lemons. Season the chicken breasts with salt and pepper, then generously season with the Montreal Chicken seasoning. Add the chicken to the bag, close, and let marinate for 15-30 minutes.
In a large bowl, add the zest from the lemons, the butter, garlic, and basil. Set aside.
Grill the chicken in a grill pan or on an outdoor grill until cooked through and it reaches an internal temperature of 165° F. Remove to a cutting board, cover with foil to keep warm, and allow it to rest while your pasta cooks.
Cook pasta in salted water according to the directions on the package, drain and add to the bowl with the lemon zest, butter, garlic, and basil. Let the pasta sit for 2-3 minutes before stirring so that the butter can melt, and the garlic is warmed.
Slice the chicken breasts into thin strips.
Toss the pasta in the bowl to coat in butter and the other ingredients. Taste for seasoning and add salt and pepper as needed. Add the parmesan and toss again to incorporate.
To serve, place pasta on the dish and top with slices of chicken and extra parmesan if desired.