Set a steamer basket in a large saucepan; fill with enough water to come just below basket. Bring to a boil; add green beans, cover, and reduce to a simmer. Cook until crisp-tender, 4 to 6 minutes.
Meanwhile, in a large nonstick skillet, heat oil over medium-high. Season chicken with salt and pepper. Working in batches, cook chicken until opaque throughout, about 3 minutes per side. Transfer to a plate, and loosely tent with aluminum foil (reserve skillet).
Place mushrooms and 1 tablespoon butter in skillet; season with salt and pepper. Cook, stirring occasionally, until mushrooms are tender, about 7 minutes. Remove from heat, and stir in remaining 2 tablespoons butter, lemon juice, and parsley. Top chicken with mushrooms, and serve with green beans alongside.