But for what purpose or mission? His killing of Culber makes no sense unless he was programmed for that purpose, but why would he be? What strategic goal is served by killing Culber? I though L'Rell and Voq wanted to defeat Kol, well that pretty much happened without any trigger words needing to be given.
Kol's faction gained the lead in the Empire with the help of a single supertech, the cloak they stole from Voq's faction. But in "Choose Your Pain", we see L'Rell interrogate Lorca to find out what the superpower of his ship might be - and then vector the already transformed Tyleroq to Lorca's ship. It seems evident that L'Rell wanted a supertech of her own, for besting Kol, and it seems logical for her to try and insert an operative to wrestle that supertech from Starfleet.
Winning or losing the Fed war was immaterial to L'Rell and probably also to Kol: just having the war would suffice for the Klingon political needs, as usual. So Tyleroq could bide his time until it became possible to hand over the ship or its secrets to L'Rell. Several ways to achieve that:
1) What transpired. L'Rell ends up aboard Tyler's ship and awakens him, and the two make away with the loot. L'Rell had a good thing going in pretending to defect, and there would have been many opportunities for her to arrange for such an opportunity. But precious few to make sure she got delivered to Tyler's ship specifically. Did she calculate that defecting while deep within Klingon space would ensure the ghostlike supership would be the one to spring her out from her "captivity"?
2) Wait till Tyler has completed gathering the necessary intel, unawares, then somehow arrange for a meeting where Voq can be awakened and debriefed. This would probably also be within L'Rell's means, especially if she weren't held captive by Kol, but in charge of a prison ship or a surgical wonder facility or both.
3) Have Tyler be first carefully embedded, then visit him to awaken Voq (for those memory lacuna moments during which he would gather intel or prepare the Discovery for taking) and then leave (or get executed by Starfleet, whatever) so that the plan would gradually come to fruition, not immediately after the awakening.
Of course, nothing seems to have gone quite according to plan. But alternative #1 sounds like the most robust plan, as L'Rell the skilled spook would presumably have lots of hooks on the Discovery after letting Lorca and Tyleroq escape. She could decide at her leisure upon her preferred means of boarding that ship, being aware of many of its weaknesses (no reason to think she aborted Lorca's torture before she got all the goodies she wanted).
That the Tyleroq transformation precedes the capture and interrogation of Lorca need not mean much. L'Rell was just hunting for some sort of a techno-edge: Lorca might have been the umpteenth Starfleet officer she captured, over a course of several months (there's a bit of leeway there), and the first to yield something she could apply her Tyleroq ruse at.
Timo Saloniemi