Amphiumas as 'lamper eels'
To follow up on Erik Kowal's excellent suggestion, I note the following entry from a list of salamanders and sirens found in Tennessee in Report of the Reelfoot Lake Biological Station, volume 12 (1948) [combined snippets]:
2. Amphiuma tridactylum Cuvier. Lamper eel. (Benton County), Lake County, Obion County, Shelby County. This salamander occurs in ponds, lakes, and, rarely, slow streams of both uplands and river bottoms. Specimens observed during the day were always in shaded areas. More were noted at night and occasionally out of the forested regions at a distance of as much as thirty feet. A mud or muck bottom and permanent water seems a requisite. Specimens were on a very few occasions found partly or entirely out of the water on mud or muck at the water's edge.
In Shelby County an apparently healthy individual was observed on January 12, 1936; and dead ones were found after a flood and freeze in February, 1937; otherwise, none had ever been found before the first week in April of any year until 1947, when both Amphiuma and Siren i. nettingi were out on March 19. The "time of emergence" does not seem to be correlated with any specific temperature in one pond under observation, although there are not enough observations to be sure. However, the animals do appear immediately after the development of a 3.5 C. thermocline.
During the first month after appearance, Amphiuma showed little tendency to move about and was often observed repeatedly at night with the forepart of the body protruding from a particular burrow in the bottom of the pond or slough. Upon being startled they always escaped by backing into the burrow. Later the Amphiuma practically deserted their burrows and wandered freely in the vicinity.
You can read Wikipedia's brief account of the amphibian (which does not mention the common name lamper eel) and see a photograph of it here. Multiple photos, some showing its tiny forefeet are collected here.
As for their dangerous reputation, a page on the Western Connecticut State University website dedicated to the two-toed amphiuma (Amphiuma means) suggests that the reputation is not entirely fanciful:
Commonly called the Congo eel, or the lamper eel, amphiuma is not an eel at all, but an amphibian; more specifically, a salamader. The misnomer of eel is well-deserved however; long and slimy, amphiumas possess four minute, all but useless limbs. Despite this, these are the only amphibians that pose a physical (as opposed to chemical) threat to humans - they have strong jaws with a double row of razor sharp teeth which can deliver a savage bite (Smith, 1877, p. 20). Further adding to this frightening arsenal, amphiumas can grow quite large (just over 1 meter), making them the largest amphibians in their range. The three species of Amphiuma can be distinguished by the number of digits on their tiny limbs: pholeter has one toe, means has two, and tridactylum has three (Conant and Collins, 1998, p. 425).
Mudpuppies as 'lamper eels'
It seems at least possible that this critter (the three-toed amphiuma) and not the similar-looking common mudpuppy (Necturus maculosus) is responsible for the most overwrought stories about "lamper eels." However, the WCSU site is somewhat misleading in implying that Amphiuma species are the only biting salamanders. Mudpuppies have teeth, too—they just don't use them for stabbing or cutting prey. As Carl Gans & Ronald Nussbaum, "The Mudpuppy: Visceral Organs" (1992) suggests, a mudpuppy may look somewhat lamprey-like when clamping down on a future meal:
The morphology of the digestive system reflects the carnivorous habits of the mudpuppy. The mouth is terminal. Its sides have interlocking labial folds, which serve to seal the lips tightly when the mouth is closed and form a basket to trap food during the "gape" phase of "suck-and-gape" feeding. Unlike mammals, such as the cat, amphibians lack facial muscles along the upper jaw.
The numerous, needle-like teeth are grasping structures that can hold struggling prey. Such teeth do not cut or crush; rather, the food must be swallowed whole. Lack of cutting and crushing teeth limits the size of prey on which mudpuppies can feed.
Various siren-like salamanders have been termed mudpuppies, mud eels, conger (or Congo) eels, and lamper eels. The names vary from locality to locality, and the same person may even apply "lamper eel" to multiple species. But whether the amphibian thus named is a mudpuppy or an amphiuma, "lamper eel" is almost certainly the source of "lanapeel" in your ex-wife's terminology.