There are many versions of Laozi. I think the book Laozi appeared after Confucius or later in the Warring States period.
First, writing books was not popular in the Spring and Autumn Period, and the ideas of Confucius and Mozi were compiled by disciples.
Second, the book Laozi is full of the colors of the Warring States period. Laozi's theory, most importantly, is anti-intelligence. ) Anti-radicalism (small country with few people) and anti-tourists and diners (except extreme, the venue is very rough) are aimed at the phenomenon at that time.
The change of academic thought in the Warring States period, from Confucius and Mozi to Xunzi and Han Fei, is precisely a reaction of the gradual decline of the aristocratic class and the gradual rise of the common people. The ready-made Laozi thought should be in the period of Xun and Han Fei.