Does it count as a 'lie' if it is believed by the parent?
There are senses of the word that include that, but I meant mostly things parents say knowing they're false, or at least that they'd admit were false if questioned.
In that case, I wonder if religion counts as a lie. Lots of religious people either truly believe, or have done a great job of tricking themselves into thinking they believe.
Much religious belief has a special protected status, though -- you aren't supposed to ask bare questions about the truth value of religious statements, or tell the truth when talking to someone else's kids;
Little jimmy: "doing that makes the baby jesus cry"
Adult: "Don't worry, Jimmy. Jesus is dead."
And the alternative: those who've tricked themselves into "not believing," but're still in the same reality tunnel, with the wall furnishings taken down but the same core dogma.
But there's certainly also the possibility that the parent thinks he believes it, although all of his actions and other beliefs reveal that he doesn't believe it.
Daniel Dennett has addressed this well. No one debates the existence of Mt. Everest, and nobody has to assert that they believe in it. To identify yourself as someone who believes in something, there must be some question as to whether or not you would. People who say they believe in something which is at the core of their group identity, and for which there is no strong evidence, are rather obviously choosing not to question those beliefs the way they would question any other belief -- including the very similar beliefs of other people's religions.
So the fact that the parent "believes" in holy reincarnation or holy levitation or holy mindreading doesn't necessarily mean that he is being honest when he tries to raise his kid to believe in such things. Do they really believe those things to be real the same way they believe Mt. Everest to be real? If not -- if there is any hiccup to his belief -- then he is lying to his kid as well as himself.
There are senses of the word that include that, but I meant mostly things parents say knowing they're false, or at least that they'd admit were false if questioned.