In a large pot of boiling salted water, cook fettuccine, stirring occasionally, until al dente according to package directions. Reserve ½ cup pasta water before draining.
Meanwhile, in a large, high-sided skillet over medium heat, heat oil. Add mushrooms and cook, stirring occasionally, until deeply golden, 15 to 20 minutes; season with salt and black pepper. Add garlic and cook, stirring, until fragrant, about 1 minute more.
Add wine and bring to a simmer. Cook, stirring occasionally, until reduced by about half, 1 to 2 minutes; season with salt, black pepper, and red pepper flakes. Add butter and stir until melted. Add capers, parsley, and lemon juice and simmer, stirring occasionally, until slightly thickened and warmed through, about 2 minutes more.
Add pasta and ¼ cup reserved pasta water and toss to coat, adding more pasta water as needed if pasta feels too dry.
Divide pasta among bowls. Top with parsley.