You should probably focus on teaching your child a more 'defensive' form of lying. It's understandable that you'd be worried about a child learning to lie all the time, but you should consider the advantages that effective lying can have, especially in modern society.
If you're planning to educate your child properly on philosophy, they should probably be taught to lie when confronted by the thought-policing left. If your child learns to properly parrot leftist ideals without believing them, they can avoid the consequences of "wrongthink" and reap all the benefits of a private education.
So, as others have said in this thread, teach your child to lie in practical, harmless ways.