People have highlighted the fact that we don't see the mother of David Sheppard (Jack's son) in the episode Lighthouse. Some people just assumed it was Sarah (Jack's hot ex-wife from the original Lost timeline)...but then, we dont see any pictures, and there is absolutely no mention of her. We can interpret that Jack is divorced / the two parents dont live together, because David is slightly estranged from Jack and only sees him a few times a month. and he clearly hates hanging out with his dad.
I was thinking, what is significant to Jack about the name David? Nothing! Nobody in the Sheppard family had any major connections to a David that we see on the show. The only people that had connections to a David....or, a DAVE... was Hurley and
....
LIBBY. Libby says in the episode "Live Together, Die Alone" that her husband was named David, the one who named his sailboat after her before he died. My theory suggests that in the flash sideways, Libby bears a child (maybe even anonymously??) with the other parent being Jack, and she dedicates to the baby the name of her ex-husband: DAVID.
to make things stretch even further, we can go to say that David (Libby's ex-husband) is actually Dave, Hurley's imaginary friend. we now know very well Hurley is not crazy after all, and he can in fact communicate with the dead. If Libby knew this, it could explain she happened to be following Hurley around in the mental ward, and why she clung onto him so quickly on the island. She saw him as a communication tool to her dead husband.
TO STRETCH IT EVEN FURTHER, considering that we now know that "love" triggers a flash sideways in the characters, maybe if Hurley sees Libby sometime in season six, he will remember how she died on the island timeline, and finally be able to ask her what her crazy story is.
what do you think!
ps. just a crazy idea, i never read spoilers and if im getting close to something dont acknowledge / deny!! just using my imagination and intuition!!