Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente. Reserve ½ cup of pasta water, then drain.
Season the chicken strips with salt and pepper. Heat olive oil in a large skillet over medium-high heat and sear the chicken for 4–5 minutes per side, until golden and cooked through (165°F internal). Transfer to a plate.
In the same skillet, melt 1 tablespoon butter and add the mushrooms. Cook for 5–6 minutes, stirring occasionally, until browned. Add the garlic in the last minute and cook until fragrant.
Add the asparagus to the skillet and cook for 3–4 minutes, until bright green and tender-crisp. Remove the vegetables and set aside with the chicken.
In the same skillet, melt the remaining 1 tablespoon butter, then whisk in the chicken broth and heavy cream. Simmer for 3–4 minutes, until slightly thickened. Whisk in the parmesan a handful at a time until smooth, then stir in the lemon juice.
Return the chicken and vegetables to the skillet along with the drained fettuccine. Toss until everything is fully coated in the sauce, adding reserved pasta water 1 tablespoon at a time if the sauce looks too thick.
Taste and adjust seasoning with salt, pepper, and red pepper flakes if desired. Divide into bowls, top with extra parmesan and parsley, and serve immediately.