In such situations, I believe the man can offer to break off the engagement, but it can only be done with the woman's consent.

So Edward could suggest it to Lucy, but she'd have to agree. Although I think she could just tell him she wanted to end it and that would be an end of it? I could be wrong here, because Cynthia feels bound to Mr Preston in Wives & Daughters. I'm not sure quite how binding an engagement was? But does not Jane F write to break it off with FC in Emma? Not quite clear on this, but I think it's important to understand the etiqutte surrounding this to understand EF's situation!