I take your point, but they do better when no one figures out it’s a lie. She knew he was lying when she saw him, and anyone would, 5’2 is not 5’7, and it should immediately raise questions, even if she’s ok with a man lying about height, “have you lied to me in other ways to persuade me to meet you?”

This doesn’t build from your point but it’s not just an integrity thing, there’s a disrespect to lying to someone because A. in this instance, you are taking their time which they might not have given you if you told the truth, B. it clearly indicates that you thought you could get away with lying/the other person wouldn’t be able to figure it out C. it has implicit that the liar has a better sense of what the person they’re lying to wants, that they will prefer a fiction to the truth and makes the decision for the person lied to about what they expect they will want. There are plenty of women fine with short men, there is a presumption that this woman in particular would care and prefer him tall when she might not care at all.