I don't think mouli lied to Mishti abt meeting pari. She told the truth and mouli said sorry and they patched up. Mouli staying away from Kunal and pari is not a good a nd perment solution . Mishti can say they can't come to Malhotra family
I think the reason mishti hates mauli as of now is cos she sees her mom giving inportance to kunal n pari. Where as time ad again the kid has been taking promises for her mom to stay away from them.but instead she sees her mom lying to her to meet pari, petting pari her infront of her.Either mauli should stay away from kunal n pari, or atleast try to understand why the child is making such a unusual demand.As a mom if she cannot understand a simple insecurity of the child. In one of the scenes mishti even tells pari , yahaan sab acche hai, tum ise bhi lelo or something.