I am he who used to be known as Duskreign’s Minion, but now I have my own (much cooler) name.
How is lying, bluffing, and generally being deceitful handled? How would a PC or NPC detect such attempts? The only mechanism I see is a reaction roll.

I think lying NPCs is a perfect example of a space in which rules make the game less good.

Agreed. I fully expect the DM to lie to the PC’s at whim and according to plot. But adjudicating when the PCs lie to a NPC can be important, especially when they fail.

I don’t think a PC could “fail” to lie to an NPC unless the NPC had evidence of the lie, and in that case, there’s nothing to adjudicate. The NPC just reacts accordingly.
Secondly, a lot of this can be handled with the Reaction Roll. But, it has little to do with whether the PC is lying or not. They could be lying and the NPC super friendly or telling the absolute truth and the NPC be hostile.
I would think in the case above, where an NPC discovers a lie a PC told, through the course of events, that would automatically affect further interaction with them. When asking for favors or whatnot, they would get appropriate reactions.
This is how I do it anyways. There’s no “insight” skill or whatever. You just lie and the NPC will trust you unless they have reason otherwise. That’s how lies work in most cases.

How NPCs respond to a player is handled with a Reaction Roll. If the PC has been caught lying in the past, a negative penalty would be appropriate.
Certain spells can be used to detect lies (or at least find out the truth), such as Commune, ESP, Telepathy, etc.