Just a lamprey. And no, more than likely it was NOT invasive. To my knoledge there are no invasive/introduced lampreys in TN. There are several species that are native. They are not eels in any way. The family they belong "Petromyzontidae" and class Agnatha (jawless fishes). Jawless is what separates this species from any other. We have shocked up several Lampreys in East TN streams. They are mostly found in leaf litter along the banks. With the exception of the Chestnut, the different species can be difficult to distinguish. Lampreys native to this area (middle to east TN):
Ohio Lamprey
Chestnut Lamprey
Mountain Brook Lamprey
American Brook Lamprey
Least Brook Lamprey
Silver Lamprey
If your in Southern Middle TN, then it can more than likely be narrowed down to the:
Ohio Lamprey (Probable that this is the lamprey you saw)
Chestnut Lamprey
Mountain Brook Lamprey
Least Brook Lamprey(Populations models and your discription would dictate this species is more than likely the Lamprey you saw).
They are not bad for the ecosystem. They play important ecological roles. The parasitism by native lampreys has not been detrimental to any native fish populations.
The Sea Lampreys in the Great Lakes region is an invasive species so maybe I'm wrong , but I'd be willing to bet it is a native species.