Heat oven to 400º F. Coat both sides of the fish with 1 tablespoon of the oil. Place in a single layer in a roasting pan.
Season with ½ teaspoon salt and ¼ teaspoon pepper. Place the lemon slices on top and roast until the fish is opaque throughout, about 15 minutes.
Meanwhile, in a large skillet, melt 2 tablespoons of the butter over medium heat.
Add the walnuts. Stir occasionally until lightly browned, 3 minutes. Remove from skillet and set aside.
Add the garlic and remaining 2 tablespoons oil and 1 tablespoon butter to the skillet. Cook for 30 seconds.
Add the kale, ½ cup water, and ½ teaspoon salt and toss. Cook, covered, tossing occasionally, until wilted, 5 minutes. Stir in the walnuts. Serve with the fish.