Is it considered a lie, and is one sinful for it, when someone says to their children, "I will eat you," but then does not do so, and they do not intend the literal meaning of the word?

Lying to children is impermissible due to its severe harm to their upbringing. This is supported by the Prophet's (peace and blessings be upon him) saying: "Whoever says to a child, 'Come, here you are,' and then gives him nothing, it is a lie." Furthermore, lying to children does not fall under the three permissible exceptions mentioned in the hadith of Umm Kulthum bint 'Uqbah, which are: lying in war, reconciling between people, and a man speaking to his wife or a woman to her husband.