Your post did capture my attention, since Lao tzu is my source of understanding the universe and life. However what is in our hand from Lao tzu legacy is Tao Te Ching (Dao De Jing or Daode Jing) - The Way and Its Power, and is also known as the Lao-tzu.
Nevertheless by going trough the text of Lao tzu , you can realize that Lao tzu did not rely on myths. but it is contrary, it was based on wisdom and logic.
So i cannot link a baby boy having white hair with the great master, especially if we now that we have very limited informations about Lao tzu and only through his book that contain 81 chapter moreover there is no confirmed information about Lao tzu having white hair when he was a baby. The following is chapter one; please enjoy reading.
Chapter One
Tao (The Way) that can be spoken of is not the Constant Tao’
The name that can be named is not a Constant Name.
Nameless, is the origin of Heaven and Earth;
The named is the Mother of all things.
Thus, the constant void enables one to observe the true essence.
The constant being enables one to see the outward manifestations.
These two come paired from the same origin.
But when the essence is manifested,
It has a different name.
This same origin is called “The Profound Mystery.”
As profound the mystery as It can be,
It is the Gate to the essence of all life.