Is khulʿ valid or invalid? And what is the ruling if the husband said: "He was only lying to me so I would calm down, and it is permissible to lie to a woman to please her"?

The mentioned صيغة (formula/wording) does not validate the khul'. The ijāb (offer) must come from the husband, and the qabūl (acceptance) from the wife. If the ijāb comes from the wife and the qabūl from the husband, the khul' is not valid, because the pronouncement of divorce is in the hand of the husband. We emphasize that these phrases are not to be trifled with. Allah the Almighty says: {And do not take the verses of Allah as a mockery} [Al-Baqarah: 231]. In case of dispute, the Sharia judge will rule on the matter.