Catalyzes the reduction of sulfopyruvate to (R)-sulfolactate. Together with SlcC, provides a racemase system that converts (2S)-3-sulfolactate to (2R)-3-sulfolactate, which is degraded further by (2R)-sulfolactate sulfo-lyase. R)-3-sulfolactate + NADP+ = 3-sulfopyruvate + H+ + NADPH.