Yes! I do believe there is a connection, though I doubt he's her father. That is just irrelevant. I mean she could have been a student under Zeref's supervision, that could somehow make sense, though I don't know how she would have stayed alive with him around her unless, she was something like Mavis-before she got cursed, that is.
One more thing. They never actually mentioned that much about Layla's death other than a being an 'illness'. This makes it fishy. Because believe me, when a story is over with, all details would have been given, and here they haven't given details. Besides, Lucy needs some heart-moving calamity for her to get powerful, though the Tartarus thing made her better, she still has a long way to go. Something about her mother being involved-killed by Zeref for example(just a suggestion), would be so good. It would do the same as it did to Gray when losing Silver.