It is a lie to tell a child that he or she can be medically and surgically altered to become the sex that he or she is not.
It's not about this though. You are stuck in a logic loop that you have constructed based on a really narrow set of assumptions that correspond to your own experience .
We need to simplify the conversation significantly.
A 6 year old tells you- when you call me a boy it causes me acute pain- I'm telling you I am a girl.
I am a girl with a penis- this is my reality. .
All you need to do is to hear them, to listen, and to understand that their experience is real . It may not be your experience. It may not be your understanding of what a girl is. That doesn't matter. What matters is the person in front of you.
The person in front of you is not a lie. They are real; their experience is real. If they grow up to have surgery it won't be because they think it will change anything about who they are or how they were born, it will simply enable them to live more comfortably in their own body, knowing that they externally appear how they internally feel. Thats it. It's got nothing to do with "lying".