So the original Tyler was on the Shenzou? Wouldn't that raise questions when Lorca checked his background out?

Not only that, but Michael and Keyla (the red-haired woman with the implant on the bridge, who served on the Shenzou as well - sans implant, I assume she got wounded) would have already know him. That's why I concluded my last reply with "Presumably this would be true for the other Starfleet ship wrecks we see floating through space there as well", i.e. that the wrecks of the other, non-Shenzou vessels we see floating about have their crew manifests on board. Again, timeline: Battle of the Binary Stars happens. Surviving Starfleet and Klingon vessels leave, except for the Ship of the Dead (with Voq and L'Rell on it), which isn't completely repaired until six months later, not least because they seem to have been left on their own while the rest of the Klingon houses duke it out for supremacy mid-war with the humans. L'Rell and Voq go to the wreck of the Shenzou in order to scavenge it for usable parts to fix the Ship of the Dead some more. (That's when we get Voq finding the crew manifest and throwing it away again, as it's of no use to him.) When they return to the Ship of the Dead, Kol has shown up, won over the Ship of the Dead's crew with food and status, and wants to kill Voq until L'Rell, pretending to switch sides, suggests to leave Voq stranded on the wreck of the Shenzou to starve to death. This idea pleases Kol, and it's done. L'Rell then has herself beamed secretly to the Shenzou again as well, and tells Voq they can fix this, she has an idea of how to win the war and have Voq instrumental in this so he can truly become T'Kuvma's successor, but he'd have to sacrfice "everything" for it. And that's the last we see of Voq. Next time we see L'Rell, she's supposedly in charge of a prison ship with one Ash Tyler on it, who says he's been her prisoner ever since the Battle of the Binary stars, all seven months.