Toss the chicken with the lemon pepper seasoning. Cover and let marinate for at least 30 minutes or up to 4 hours in the refrigerator.
Heat a large skillet over medium high heat. Add the olive oil and swirl to coat the bottom of the pan. Add the chicken and cook for 4 minutes or so. The chicken should be light golden. Remove the chicken from the pan and reserve. Leave the drippings in the pan.
Add the onions to the pan and saute for 3 minutes or until the onions begin to become translucent. Add the garlic and cook for another minute or so.
While you prepare the vegetables, cook the pasta in boiling salted water for 2 minutes less than the package directs. Drain and set aside.
Add the asparagus to the pan and cook for 3 – 4 minutes. Toss frequently to insure even cooking. Add a little chicken broth if things seem dry.
Add the vermouth (or broth) and the juice of the lemon to the pan. Lower the heat slightly and allow to cook for 3 minutes or so.
Add the Italian seasoning and the lemon zest, stirring to combine. Return the chicken to the pan. Toss to mix evenly.
Add the olives, tomatoes, and pasta to the pan and continue to cook 3 minutes or so until everything is heated through. Taste for seasoning and add salt and pepper if needed.
Spoon the mixture into a serving bowl and sprinkle with the feta cheese and serve.