Phew, this took a while. But I'm pretty proud of the result and it was super fun to work on!
So this is sort of a HopeRai timeline. From bottom to top we have their summon crystals, fighting as L'Cie, crystallized Cocoon, Valhalla!Lightning, and a shippy moment between Lightning and an adult Hope - perhaps after the events of whole story.
While I don't ship them together in XIII, I do in XIII-2 when Hope is older. I really love their relationship as 'guardian and student' throughout XIII, though. Their relationship in a whole is great, actually. They seem to depend and trust each other a huge amount, and when Hope is older their personalities would blend really well to create a wonderful couple.
Also, they're damn pretty together.
Hope and Lightning are from Final Fantasy XIII | XIII-2