The best part about that is that Emma won’t tell Henry the truth. Not after she has already woven this lie and he bought it. So all he’d know is that Emma is keeping him away from this stranger who he’s already friends with (and you all know how well he listens to parents when it comes to who he hangs out with 😉 ).
I think if they are friends before the truth comes out, the fact that Emma was lying will only hurt more. Especialy if Henry can’t see why she would lie.