Wondering if the order of the lotting corresponds with the order that your furs are tagged. I was hoping that the tag number would be noted with the lot number, as I wanted to know how the grading worked.

If you are referring to a state issued tag , no they don't. The lot number is tied into the grade of the skin. The closer to the top of the list the better.

Lot numbers change from sale to sale. If you click on your lot number it will usually open up to the page in the sale sale catelog.
Here you can see how your pelt did compared to others.

The scan tags are used to identify your skins. Once all the pelts are lotted then the scan tags of all the skins in each lot are read and entered into the computer. The lotting letters are then produced advising the shipper of where his pelts are, in which lots and what grades.