Actually, there is grave doubts, among historians, Western and Eastern alike, as toward Laozi ever existing.

However, since Confucius references him three times, as far as consulting him regarding burial rights ... it may give credence to his actual existence. Yet, on that one ... according to legend, pursuant to the birth date of Laozi, he should have been dead by that time.

If one does buy into him having been alive, the only reference to his writings were two ... a very brief overview of the Tao and another that he supposedly wrote, at then China's border, at the insistence/request of the border's general.

So, whether Laozi wrote everything or it was written by others, following the Old Master ... it's a good read,