There's a Mrs. Lovett thread in the Character Discussion Forum, but anyway.
I think it was just jealousy because nobody probably paid any attention to her when Lucy and Sweeney still lived above her shop, though she was in love with Sweeney. It kind of makes sense that she'd want him all to herself since Lucy was out of the way.
I might've done the same, but it depends on the secret and the person. ;D