Heat oil in a large skillet over medium-high heat. Add onion and mushrooms. Cook for 7 minutes. Add garlic and crushed chile flakes. Cook for 1 minute.
Stir in salt, broth, and pasta. Bring to a boil. Reduce heat, cover, and cook at a simmer for 10 minutes, stirring halfway through.
Turn off heat. Add spinach, cover, and let sit for 2 minutes. Stir in Parmesan and lemon juice. Serve immediately.