Heat 1 tablespoon butter and 1 tablespoon olive oil in a large deep skillet or Dutch oven over medium-high heat until the butter melts.
Add the chicken strips, sprinkle with 1/4 teaspoon salt and 1/8 teaspoon pepper, and sauté until golden and cooked through, about 5 minutes; transfer to a plate and cover to keep warm.
Reduce heat to medium and add the remaining 2 tablespoons butter and chopped onion; cook until the onion softens, about 3 minutes, avoiding browning.
Add the minced garlic, Italian seasoning, red pepper flakes, and the remaining 1/4 teaspoon salt; stir and cook until fragrant, about 30 seconds.
Slowly stir in the chicken broth and milk, bring to a boil, then add the ziti; boil 5 minutes, stirring occasionally.
Stir in the broccoli florets and continue boiling until the pasta is al dente, about 5 to 7 more minutes, stirring often; add more milk if the pan becomes too dry.
Stir in the drained artichoke hearts, lemon juice, Parmesan, chopped parsley, and the reserved chicken; taste and adjust seasoning as needed.
Serve hot with extra Parmesan and parsley sprinkled on top if desired.