Ultimately, Derek knew that holding her hand as she fell asleep wasn't much of anything, but when he'd lost everything, all at the hands of someone he'd thought cared about him, it had been nice. It was a small reminder that he wasn't as alone as he felt. He didn't know the root of Lydia's problems. He wasn't going to ask her now, but if it helped, he could survive a night without being a wolf.
Shifting a little once he had her hand, he let himself fall still again. As far as he knew, that was the extent of what he actually could do. He was strangely okay with watching her now and listening to the sound of her breathing, tilting his head back against the back of the chair.