Let's play a little game of "whose bug is this?" This famous game goes back to the very first days of computers, when hardware and software engineers would argue that the problem being experienced couldn't possibly be their fault. Today's contestants: Nikon and Adobe.
Nikon will say the D3s not tethering with Lightroom is an Adobe problem. Adobe will say it's a Nikon problem. Who's right? Well, here's a clue: try erasing the cards in the camera. That's right, they were full. Seems that the camera will tether with NO card in the camera, and it'll tether with empty cards in the camera, but if the card(s) in the camera is full, then the D3s and Lightroom will refuse to cooperate with one another. Still confused about whose bug it is? So are Nikon and Adobe. But fortunately, you now know the answer to your problem, so you're happy, right?
The other answer to this question is that Lightroom Classic version 6.x is fixed in time, it isn’t updated for new cameras (e.g. D780, D6, etc.). You need to make sure you’re using the latest version of Lightroom CC Classic in order to tether, and even then it sometimes takes Adobe a couple of months to catch up to the latest camera releases.