Do you have the NPC make a deception check vs. the PCs, and if so, do you roll secretly?

Or, do you wait until the one of the players asks "Do I think he's lying?" and roll deception at that point, or should I let the players roll discipline vs deception?

I let my players initiate it. If they don't ask if he's lying, oh well, it makes for a more interesting story.

So, they ask if he's lying, I have the pc make the discipline check. Convert the npcs Deception (Cun) into difficulty dice, add in some upgrades, setbacks and boosts and watch the fun.

Discipline doesn't so much detect lies as it prevents being manipulated by lies. If the liar isn't trying to get you to do something, then Discipline doesn't really help.

For example, a character stating that he's from Tatooine and is an only child may be lying or telling the truth. Disciple wont tell you either way. When that character tries to convince someone to take an action through Deception then Disciple can prevent taking that action, but it doesn't really act as a lie detector.

Which abilty do I roll for detecting lies?

It really depends.

Cool is used with gambling to help see through bluffing. Perception may notice body language tells that they are lying. Same could go for Vigilance. Knowledge(topic) to factually catch them in a lie.

Many skills could apply, depending on the situation.

I usually default to Perception, but Tear44 makes a good point about using other skills if they directly relate to the subject at hand.

In any case, the player always rolls, and everything is open.

I had a slight twist on this the other day. The player was trying to convince an NPC of something that was true, but they didn't believe. The mechanics are normally set up for PCs lying or being lied to, and normally the PC rolls the dice. In this case the NPC was doing the "lie-detection", but the PC wasn't actively trying to manipulate. So I built the dice pool (Perception for the NPC vs Cool for the PC) but then had the PC roll.

(Net result was a single Despair, which played out very well for the PC…starting with a Zeltron sobbing in his arms and promising to do everything she could to help him in his troubles… )

Typically if one of my characters asks if they can make a roll, I'll always tell them yes. Doesn't mean that the person in question is telling the truth or lying, but i'll let them. Sometimes i'll roll for them, but sometimes not. it really depends on what the players are trying to accomplish.

Which abilty do I roll for detecting lies?

There's no Sense Motive, for a good reason.

Is the guy lying about what a certain drug could do for you? Try Medicine. Lying about a Gammorean's favorite food? Knowledge: Xenology. Virtually every skill could be implicated in knowing true facts.

If you mean, how do I detect that an NPC who says "this corridor is safe, head that way" is leading you into an ambush? I'd probably go with Perception or Cool.