@Quickleaf, I don't know how much 5e D&D play takes place at 20th level, so I don't know how important balance considerations are. But to me it seems the most natural fighter equivalent to Stroke of Luck is Stroke of Death: once per rest, your attack kills the creature you strike.
Well, I think balance considerations are important enough that this would be utterly bonkers, and I'm pretty sure not fun to most players either to big boss monsters always getting killed this way.
One thing I miss from 4e is the bloodied value. It was handy for keying all sorts of mechanics into.* For example fighter could have a feature that if they dealt at least the enemy's bloodies value's worth of damage with one strike, it would be an insta kill. And if you wanted to make this even more powerful, you could accompany it with the ability to choose to do one powerful strike instead of many regular ones.
*Now you can of course just refer to "half the hit point maximum" but as that is not a value that actually is written anywhere in the statblocks it is a bit more awkward.
Replying to you both, cause my mind linked your comments. Yes, I think you're honing in on something that relates to the undercurrent of the conversation – that 5th edition is microtransactional. At 20th level, I think it's fair to break that a little, though I agree it's not worth getting lost in designing a hypothetical 20th level feature.
I think the general idea of a Stroke of Death is awesome, and of course to 5e-ify it would require certain limiting language be added, eg. "...creature with legendary actions or legendary resistances cannot be reduced to 0 hp by this effect; instead they take an additional 6d8 damage from the attack." Something like that.
To get back to the microtransactional design, if you look at a Battle Master maneuver that gives an effective attack bonus like Feinting Attack (gain advantage), it's still falling short of saying "You spent a resource? Great, you can automatically hit!" instead 5e says, "ok, you can have an improved chance of hitting, but if you miss, sorry."
My opinion is that this microtransactional paradigm impacts the combat side of things more than the other lighter weight systems in the game because combat is microscopically detailed (in comparison). And the fighter IS almost entirely built around combat, so any design is trying to squeeze in effects with micro-steps, and this "squeeze" effect on design intensifies at higher levels as the designers walk this microtransactional design railroad that leads to ...well, a very popular class ...but also a small subset of folks (raises hand) who find it myopic.