The fossil mammal genus Lophiodon has a complex taxonomic history, which records the likes of many valid species, synonymous species names, and species that were eventually reclassified to other mammal genera. Its taxonomic history dates back as early as 1804 when the French naturalist Georges Cuvier referred to some of its first studied fossils as belonging to tapirs before eventually being assigned to new species of Palaeotherium by him in 1812. Although first recognized as a distinct genus by French zoologist Henri Marie Ducrotay de Blainville, who gave it the name Tapirotherium, the name Lophiodon, deriving from the hill-like cusps somewhat like in tapirs, as given by Cuvier in 1822 became more widely used without its validity being overridden by the preexisting genus name at any point. Although Cuvier recognized many potential species of Lophiodon, later palaeontologists like the French zoologist Johann Baptist Fischer assigned them to formal species names.

Many species in Europe and North America were assigned to Lophiodon in the 19th century but were eventually classified to various other mammal genera like other members of the Lophiodontidae as well as to other members of the Perissodactyla and to Coryphodon. There are fourteen species presently assigned to Lophiodon in total, although L. glandicus remains not as well-defined while "L." sardus is pending revisions to another genus and is not considered to be a Paralophiodon species despite having been previously reassigned there.

Early taxonomy Cuvier's documentations and early taxonomy

Fossils of Lophiodon have first been studied in 1804 by the French palaeontologist Georges Cuvier, who originally referred to some of them as belonging to a small-sized tapir (with some close relatives also being studied by him before 1822). In 1812, he erected within the extinct genus Palaeotherium the species P. giganteum, P. tapiroïdes, P. buxovillanum, and P. occitanicum, describing them as being the size of rhinoceroses, oxes, pigs, and sheep, respectively. As early as 1817, French zoologist Henri Marie Ducrotay de Blainville suggested that some species classified to Palaeotherium by Cuvier like P. tapiroïdes should be classified under the new genus Tapirotherium. He suggested that it would have been intermediate in morphology between Tapirus and Palaeotherium. He said that he did not know of any upper jaw belonging to Tapirotherium but suggested that it would be similar to that of Palaeotherium. He noted a lower half of a jaw from a collection belonging to an individual named Mr. de Drée, which he said contained three incisors, a strong canine, and six molars, the last three of the latter of which he said were similar to those of tapirs and Palaeotherium.

In 1822, Cuvier dedicated an entire chapter to "tapir-like" mammal fossils found in various European localities. In the chapter's first section, he described various tapir-like teeth from several localities that he did not assign any name to and referenced several other localities that he would then describe in the next section. Among them were dental material from the French city of Orléans that he assigned to the informal name "tapir gigantesques", or "gigantic tapirs." In the second section, Cuvier erected the genus name Lophiodon, stating that its name references the transverse hill-like cusps of the molars like in modern tapirs. He also stated that like tapirs, Lophiodon had six incisors and two canines on each side of its mouth (or three incisors and one canine in each jaw's side). Cuvier argued that it differed from tapirs in having more oblique cusps in each molar, there being one rather than two cusps in each of the first molars, and the bases of the molars being less rectangular (especially the last ones). Furthermore, he said that some species of Lophiodon had different tooth morphologies more reminiscent of hyraxes and rhinoceroses and thus form a diverse range of forms by species like Palaeotherium. The genus name Lophiodon means "crested tooth", which is a compound of the Greek prefix () meaning 'crest' and the suffix () meaning 'tooth'.

In the second volume of a research book series in 1822, Cuvier described fossil remains he suggested belong to Lophiodon, proposing that there are multiple species but not assigning species names to them. The first species he described, "average" in size, was originally unearthed from the French commune of Issel within the department of Aude. Cuvier stated that the collection of fossils belonging to this particular species was held by the nobleman Philippe-Laurent de Joubert then studied by Cuvier himself a few years before writing his research. Describing fossil jaws, femora, and tibias, Cuvier wrote that it would have analogous to tapirs and was nearly the same size as the South American tapir. He also said that there were two other species of Lophiodon at Issel; one was smaller in size, had slender legs, and was known by a partial jaw and heads of a femur and tibia. The other, he communicated, was larger than the other two species and was known only by postcranial evidence consisting of a femur, humerus, scapula, ulna, and astragalus.

He also described several species from the commune of Argenton-sur-Creuse, located within the French department of Indre. An inhabitant named Mr. Bollinat had collected fossils from his workers at a marl pit and sent them to a king's cabinet under the invitation of the French consul Charles Étienne Coquebert de Montbret. Cuvier mentioned that the dentition of the first described species of the locality, large in size, closely resembled those of Issel, and were similar to rhinoceroses as well. He also assigned a radius and a humerus to it. Cuvier also admitted that it was so similar to the large species from Issel that he could not discount the two individuals being the same species. The second species of the locality, Cuvier continued, had smaller teeth than the first, was known by dentition only, and would have been the size of a Malayan tapir. He also recorded a small species and another very small species from dental evidence (the former of which he stated was also known by a fragmentary astragalus and ulna).

Cuvier then described additional fossils assigned to Lophiodon that were found in the freshwater limestone in a hill range called Vosges (more specifically the Bastberg Hill), located near the French commune of Bouxwiller (or "Buchsweiler") within the department of Bas-Rhin. He wrote that the late French geologist Barthélemy Faujas de Saint-Fond had notified him of the fossils seen in the studies of the then-deceased French naturalist Jean-Frédéric Hermann; Hermann's son-in-law, Frédéric-Louis Hammer, lent him his father-in-law's fossil collection and added in more fossils found from the original site. Cuvier then listed a large-sized species (larger than the Malayan tapir and large-sized species of Lophiodon at Issel and Argenton) known from a partial lower jaw and a fragmentary femur, previously named P. tapiroïdes, and another smaller-sized species known only from dental fossils that he said was previously named P. buxovillanum.

The French naturalist then listed another species known from a last upper molar from the French commune of Soissons in the department of Aisne, suggesting that it was related to the large-sized species from Bastberg and Argenton. Another species he recorded was a tooth from an unknown locality, which he said may have belonged to a large Lophiodon species from the Bastberg Hill. He then noted two species from quarries of a small settlement called Montabusard in the French commune of Ingré in the department of Loiret near the city of Orléans. He said that the fossils were collected by a merchant and natural history hobbyist from Orléans named Mr. Defay. The first species was large-sized; was known by a partial lower jaw, lower tibia, and astragalus (the latter uncovered from a quarry in Orléans by a pharmacist named Mr. Prozet); and was previously named P. giganteum. The second species, he wrote, was smaller-sized, and was known by humeri, which were before assigned to P. aurelianense. He also recalled being in the Swiss city of Geneva and finding some teeth in the office of a late man named G. A. Dulec, which were found in the French village of Boutonnet near the city of Montpellier. He additionally documented a fragmentary femur and partial humerus from the commune of Mons-en-Laonnois for the sake of not "neglect[ing] anything that could belong to this genus". Lastly, he documented a pelvis that he purchased from peasants of the valley Valdarno (or the Arno Valley), speculating that the probable Lophiodon species was larger than a Malayan tapir but smaller than an ox.

In his third research book entry, published the same year, Cuvier wrote that fossils of Lophiodon were commonly found in fossil deposits with those of Palaeotherium, a notable exception being in the Paris Basin. He also wrote about a femur found at the commune of Clermont-Ferrand that was found and lent to him by Royal College of Clermont-Ferrand physics and natural history professor Abbé Lacoste, noting that it is larger than that of the Sumatran rhinoceros and suggesting that it belonged to the large-sized species known from Montabusard. The same year, French zoologist Anselme Gaëtan Desmarest listed multiple species, all described but most previously named by Cuvier: L. giganteum and L. aurelienense of Orléans, L. tapiroides and L. buschsowillanum of Bouxwiller, and L. tapirotherium and L. occitanicum of Issel. The species name L. tapirotherium is derived from the genus name Tapirotherium from Blainville that was effectively synonymized. He also suggested the species names L. orléanais and L. occitanique to replace L. aurelianense and L. occitanicum, respectively. Additionally, French zoologist Johann Baptist Fischer listed the multiple species of Lophiodon described by Cuvier, among them the "average-sized" L. Tapirotherium from Issel whose scientific name he credited to Cuvier.

In 1829, Fischer relisted Lophiodon species previously described by Cuvier but wrote of additional species names based on the fossils that Cuvier had already described without having assigned names to them: L. Isselense of Issel and L. medium, L. minutum, and L. minimum of Argenton. Saxon palaeontologist Gotthelf Fischer von Waldheim erected L. sibiricus the same year, describing the genus as having had its name derived from the transverse ridges on its molars. L. sibiricus, he said, was found in the limestone deposits with blue copper oxide in Siberia at the Miass River at what was then the Orenburg Governorate and must have been gigantic based on its canine tooth being long. He also had portions of a femur and tibia but could not confirm if it belonged to the same species. The same year, German naturalist Johann Jakob Kaup erected the genus Deinotherium, basing it off of fossil material that Cuvier previously said belonged to "tapirs gigantesques" and reusing the "giganteus" species name for it. Therefore, all the "tapir" fossil material described by Cuvier that were not assigned to Lophiodon were instead transferred to Deinotherium.

Early 19th century taxonomy