I believe that should be a persuasion roll for the NPC, with a base DC of 10. You can decrease the DC to something as low as an automatic success (DC 0) if characters are in friendly terms, or increase it up to a DC of 20 if the interaction happens under an atmosphere of strong hostility.
EDIT: I would also apply the PC's insight skill as a negative modifier to the persuasion roll. Insightfulness should make you more adept at detecting sincerity.
I likely don't set a DC. The character succeeds, no roll, perhaps because the truthful NPC exhibits no body language, speech habit, or change in mannerisms that suggest a deception.
And this. When an NPC lies to a PC, I roll for the NPC against the PC’s passive Wisdom (Insight). On a failure, I tell the PCs what they notice - for instance, that the NPC is having difficulty maintaining eye contact and their brow has a faint glimmer of sweat or something. On a success, I let the NPC’s statement stand on its own. In either case, it is up to the player whether their character believes they are being lied to or not.This is yet another reason why using a skill to "detect" truth or lies is a terrible idea.
If a PC is unsure whether an NPC is being honest but that NPC is actually being honest, I roll the dice behind the dm screen and then Tell the player the truth that NPC seems to be sincere. I don’t even bother looking at the dice roll. I like adding that little bit of uncertainty.