Diavolo is a walking lie detector, yes?
Well, that's true to a certain extent. He can tell when people are lying with little to no difficulty.
However, there's a catch.
He has a very hard time with half-truths or people who aren't aware that they're lying.
For example:
Diavolo asks how Lucifer's doing.
He says he's fine.
He's not.
He's had a shitty week, he's barely gotten any sleep, and he's overworking himself.
But Lucifer truly believes that he is going to be okay, so he's not lying.
Diavolo wouldn't technically be able to detect this as a lie with his powers. (He can see that Lucifer isn't doing well, so it doesn't mean much)
Or, and this might be a stupid example, but bear with me.
Mammon has someone's wallet. He takes all of the cards and money out of it before handing it back to the owner.
If Diavolo were to ask, "did you give the wallet back?"
Mammon can say yes and get away with it.
Because, yes, he did. He just didn't give away the money.
This works because the person lying has convinced themself that what they're saying is absolutely true.
If he asked Beel where Belphie was (before the fight,) and Beel says, "the Human World" it wouldn't be a lie.
Because, to Beel, that's where he is. Beel isn't lying, he just doesn't know any better here.
On the other hand, if he asks someone something that they believe to be true, and it isn't, the same thing can happen.
Levi says that he's disgusting and doesn't deserve happiness and he's the worst person EVER.
It won't come back as a lie because Leviathan can spiral and begin to believe this (even if it's not the truth)
Diavolo is aware of this. He asks questions very carefully.
He might ask Lucifer if he's okay, but he knows that it won't come back as a lie. He wants to see if he'll be honest with him.
He wouldn't ask Mammon if he gave the wallet back, he would say "Did you give the wallet back and everything in it?"
The questions might be phrased really badly, and it's obvious that's what he's doing.
They can't dodge the question, though. It only makes them more suspicious.
So yes, Diavolo is a very effective lie detector.