There was another thread here recently, apparently about the same issue.
It seems that file sequential numbering only uses a persistent counter during Imports (and only when importing with "Move", or with "Copy" - since "Add" does not allow the files to be renamed at all).
According to that other thread, numbering sequence does NOT continue (cumulatively) when you are later renaming files.
As I understand it, tethered shooting does not work the same as using the Import dialog to Copy or Move. It is apparently more like an "Add". (My own camera is not supported for tethering, so I have no personal experience to report of this).
If what's needed is a sequential unique code, might a combination of the capture date and the camera image number suffice? This would deliver the same results whether done immediately or later, and no matter in what order applied to the images. It conveniently tells you the shooting date from the filename, and also allows you to easily match up the LR imported file with an archived copy of the camera original, should you have had LR make one to a second location at import - or else, to match up with the camera original which remains on the memory card.
I don't know why sequential numbering doesn't keep track when renaming, but perhaps it is because the meaning of such a sequence would not be so useful, as it is when importing. The order of such numbers could only ever denote the order in which you had renamed them.
AdChoices