Can you tell me if this is correct for second conditional, please?
"If I found out that he had lied, I would not talk to him again."
Or would you have to use the first conditional?
"If I find out that he has lied I will not talk to him again."
They are both correctly formed, the only difference is in the hypothetical-ness of the prediction.
With your first sentence, you are just explaining what you would do in a situation where someone gets caught lying to you (notice that this is a non-past action). You probably aren't thinking of a specific example, but if you are then you don't consider it to be extremely likely that he has lied. At any rate, you are expressing your general policy of not talking to people who lie to you.
In your second sentence, it seems like you suspect him of lying or you are not 100% sure he has told the truth. There is more of a specific context here and you are explaining how you will respond if this is true.