Slice the chard stems from the leaves. Coarsely chop the stems and set aside; cut the leaves crosswise into 1-inch-wide strips and set aside.
Heat the oil in a medium frying pan over medium heat until shimmering, about 3 minutes. Add the onion, anchovies, and raisins and cook, stirring occasionally, until the onion has softened, about 4 minutes.
Add the capers and garlic and cook, stirring often, until the garlic is fragrant and lightly browned, about 1 minute. Add the reserved chard stems and cook until they start to brown, about 2 minutes.
Add the chard leaves and cook, stirring the leaves with tongs, until they're wilted, about 5 minutes. Stir in the olives, pine nuts, and lemon juice, season with salt and pepper, and serve immediately.