In a large bowl, combine the tuna, breadcrumbs, olives, raisins, egg, onion and cumin; season with salt and pepper. Form into 4 patties.
In a large skillet, heat 2 tablespoons olive oil over medium heat. Add the patties and cook, turning once, until golden, about 8 minutes.
Meanwhile, in a large bowl, whisk together the remaining 2 tablespoons olive oil and the olive juice; season with salt and pepper. Add the lettuce and toss to coat. Serve the tuna cakes on the salad.