In a big pot of salted boiling-water, cook pasta according to package directions until al dente. Drain & return to pot.
In a skillet over moderate heat, warm olive-oil. Add chicken & season with pepper, salt, and Italian-seasoning. Cook till golden & no longer pink, 8 mins each side. Transfer to a plate to allow remainder, then thinly slice.
To skillet, melt butter over moderate heat. Add red-onion & simmer and season with pepper and salt. Cook till tender 5 mins, then add heavy-cream, chicken-broth, lemon-juice & garlic and simmer for 5 mins.
Stir cheese & cook till melty, then add lemon pieces and cooked linguine.
Top with chopped chicken and garnish with additional Parmesan & parsley.