Heat olive oil with butter in a skillet over medium heat. Stir in the garlic. Place fish fillets in the skillet; sprinkle the fish with salt and pepper, and cook for 90 seconds. Turn the fish; season with salt and pepper, and cook an additional 90 seconds.
Add the mushrooms, capers, and wine. Cover, reduce heat, and simmer until the fish flakes easily with a fork and the wine is reduced by half, 6 to 7 minutes. Remove the cover, pour in lemon juice, and cook for one minute.