A kid (even younger) should know the basics of how to bluff in some sort of table-game. And it should do "I pretend to be a policeman/mother/lion who does xyz" in a game. Or doing magic tricks with a straight face. All of that helps with being aware of their own mimic and gesture, and it helps being more aware of simple inter-human "tactics" that they will meet everyday.
As for protecting them from more sophisticated liars, the important "skill" is realizing that and how they can be fooled (a skill many adults still lack).
When I was a teenager, I found a book of some ufo-conspiracist. I was fascinated, and the arguments of the author seemed very conclusive. But at the end of the books there were some photos, one depicting an ancient maya stone-relief. The text had claimed that every child would recognize it as a being riding a rocketship. But when I saw the picture I realized that no sane/adult person (who had seen rocket-ships would depict them that way. I realized I had been manipulated by eloquence.
It was a very valuable realization for me: I had fallen for the author's arguments just because he was so good at spinning and verbalizing them.
It is hard to "create" such an experience for your kid. But sometimes you might get a (hopefully save) opportunity. Where your kid can read or listen to something very convincing and eloquent, but where you can clearly show how it was deceiving.
Along those lines it is also important to talk about falsehoods that are not lies. In our time, for example, there is a lot of talk about true and false information in media. Talk about how articles can influenced by a lack of (research-)time, a need to catch the readers attention, a need to please the reader and the need for advertizers money. Show some different newspapers, internet click-bait and similar things. Discuss and compare together which seems to be more trustworthy in that regard. (Edit: this paragraph sounds a bit negative. You certainly should also mention which ideals help to make media more trustworthy.)
Talk about people who believe (and tell) things because it would be too hard to accept the truth. Talk about functional psychopaths or watch a good youtube-video about them.
Also do talk about times when you have been fooled. We tend to avoid those topics out of shame, but admitting we have been fooled (and discussing why) can help the kid a lot! It also takes the stigma from admitting (to oneself in the first place) that one has been fooled.
To answer your original question: You do not need to teach lying. It might just make the kid think every liar will use their own techniques, making them more easy to be fooled. Telling your kids how you lied can be a helpful part of teaching them to spot falsehoods. But it is only a part, and it is not a skill that needs to be trained.