Normally, we wouldn't even bother to mention the author in this section. Most of the time when we're analyzing a poem, it's best to think of the speaker as a creation of the author… even if the speaker says stuff that sounds a whole lot like what the author would say.
The Tao Te Ching is little different, though, since it's not necessarily meant to be a piece of art (even though it totally is). The TTC is meant to be a guide for how to live our lives. It's a philosophical text in which the author directly addresses us and gives us tips for achieving universal oneness and all that good stuff. So saying that the author of the TTC (our man Lao Tzu) isn't the speaker would be kinda like saying Marcus Aurelius isn't the speaker of The Meditations of Marcus Aurelius.
Even though there's some debate, the author of the Tao Te Ching is most likely a super-wise man named Lao Tzu, who was Taoin' it up in China around 2,500 years ago. Legend says that he was a master scribe/librarian type guy for a king and had access to tons of ancient knowledge, including the words of many of the Tao sages who came before him. There are some historical documents that show he did actually exist, so when the TTC says stuff like "I do not know whose offspring it is," we're pretty sure the "I" is Lao Tzu himself (4.8-9).
Of course, for the most part, Lao Tzu keeps the "I" out of the Tao Te Ching. His name might translate to something like "old master," but he would prefer it if nobody put him on a pedestal. He never claimed to be a prophet, messiah, or demigod. He only claimed to be a simple man with simple wisdom to give. After all, one of the biggest lessons of the TTC is that we should practice humility and selflessness. Take these lines for instance:
The reason I have great misfortune
Is that I have the self
If I have no self
What misfortune do I have? (13.9-12)
The self is the greatest misfortune? That's about as humble as it gets. Seems like Lao Tzu would just as soon have every copy of the TTC printed without his name even on it. Maybe he's the one who started the rumors that he didn't write it. We're onto you, Lao Tzu.
So who was Lao Tzu? We can only assume that he was a man who did his lowly best to embody all the teachings of the Tao Te Ching. He was humble, generous, patient, and nonjudgmental. He did his best to live with wu wei (unattached action) and moved through life without obsessing over the outcomes of every little thing. And even if he was better at writing about these principles than he was at living them, he was a teacher who at his core cared very much about humanity and, in his gentle way, wrote a book to show us a way we could all live in peace with each other, ourselves, and the Universe.
We're thinking about starting a Lao Tzu fan club. Oh, wait... that's called Taoism.