Slice chard stems from leaves. Coarsely chop stems and set aside; cut leaves crosswise into 1-inch-wide strips and set aside.
Heat oil and butter in a medium frying pan over medium-high heat. Once butter foams, add onion, anchovies, and raisins and cook until onion is Add capers and garlic and cook until garlic is fragrant and lightly browned. Immediately add chard stems and cook until they start to brown.
Add chard leaves, reduce heat to medium, and cook until chard wilts, about 10 minutes. Stir in remaining ingredients, season with salt and freshly ground black pepper, and cook until lemon juice cooks off, about 5 to 6 minutes. Serve immediately.