He had no more control over his life than a dog on a chain, but caring for Lucy made him feel…well…strong.
He felt as if he had little control over his life, comparing himself to a dog restrained on a chain, unable to do as he wished. This imagery reflects his sense of helplessness and confinement in his situation.
Despite this lack of control, caring for Lucy gave him a sense of strength and purpose. It was through his relationship with her that he found some measure of empowerment and resilience in difficult circumstances.