Hal Runkel, with ScreamFree LLC, reminds us that from time to time this can be a problem with individual children, and especially with sibling interaction. His approach is teach them not so much that it’s wrong, but that it doesn’t work at your house.
By explanation, if a child says they’ve brushed their teeth, and you are pretty sure they haven’t, sometimes you might just say “okay”. Other times, to keep them guessing, your response might be: “brush them again”. Of course they may protest, to which you respond, “I don’t care, just brush them again!”
The point of this approach is that you as a parent don’t get drawn into a battle with them that there is no way to win.
Another area where “lying” may show up is in sibling arguments: “He started it”, “No, she hit me first”. Just like the conflicts in the Middle East, there is a history of interaction that is impossible to search out. Simply have as a family guideline, that’s known and quoted repeatedly: “When we fight, we both get in trouble”. With that approach, you are not dealing with history or hitting… simply dealing with a behavior according to the rules of the house.