Here are some ideas:
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Pay very close attention to the case so you can see if what someone is telling you makes sense or not.
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Find all the clues so that you have evidence to back up accusations of lying and so that you can do the first point.
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Watch your suspect's body language to see if they are lying; some have a good poker face, but some are pretty obvious when they aren't telling the truth.
There's no guaranteed way to tell if someone is lying or not, you just have to make your best assessment of the situation. Alternatively, you can follow these guides. They have the correct response to every question. L.A. Noire Case Guides.