Vautrin et al. 2020 published on rare Lophiaspis
(Fig 1) a less than popular and poorly known taxon.
Wikipedia reports only this:
“Lophiaspis is an extinct genus of early perissodaclotyl endemic to southern Europe during the Early to Middle Eocene, living from 55.8 to 37.2 Ma. Remains have been found from France, Spain, and Portugal.”

By contrast
in the large reptile tree (LRT, 2047 taxa) Lophiaspis maurettei (Depéret 1910; Vautrin et al. 2014, Early Eocene 43mya) nests with oreodonts. It was similar to Agriochoerus antiquus (Figs 2, 3), but with more of its anterior upper teeth reduced to vestiges. The naris opened ventrally. That’s a rare morphology for placentals, convergent with humans. The upper molars were flattened with little to no lateral exposure. In lateral view the skull was streamlined like a bullet.

Originally and recently
(e.g. Vautrin et al. 2020) Lophiaspis was considered a primitive perissodactyl and a relative of the basal tapir or a basal chalicothere (Bai, Wang and Meng 2018). In both studies Lophiaspis nested with what they thought was a basal tapir, Lophiodon (Fig 4, actually a marsupial), based largely on convergent tooth traits and taxon exclusion. Vautrin et al. 2014 omitted Agriochoerus and oreodonts from their study that focused only on basal perissodactyls to the exclusion of other placental mammal taxa.

Bai, Wang and Meng 2018 likewise nested Lophiaspis
with perissodactyls by cherry picking taxa and omitting oredonts from their taxon list. These authors nested Lophiaspis with chalicotheres (aka Ancylopoda). These authors also nested the basal pigs, Lambdotherium and Danjiangia with brontotheres while omitting pig ancestors like Cainotherium. These authors also nested the desmostylian ancestor and derived hippo, Cambaytherium with the basal elephant, Radinskya, by omitting hippos, desmostylians and elephants. The LRT minimizes taxon exclusion by including so many more taxa that prior, more focused studies.
Vautrin et al. 2014 reported,
“The Lophiodontidae are endemic perissodactyls from Europe that flourished during the Eocene.
When more taxa are added Lophiaspis (Fig 1) is not related to Lophiodon (Fig 4) or perissodactyls. So the rest of this abstract describes an irrelevant clade.
“Despite their preponderance in the European fossil record, their exact origin and relationships within the perissodactyls remain unknown due to the rare and fragmentary material in the early Ypresian, the time of their earliest radiation. Lophiaspis maurettei is the oldest and earliest diverging lophiodontid known to date but is unfortunately poorly known.
The oreodont clade is more primitive than the clade Perissodactyla in the LRT.
“We describe here the results of new excavations of the type locality of Palette. Important new material including complete skulls, mandibles, post-cranial elements and juvenile specimens lead us to revise Lophiaspis maurettei from Palette and other localities and to describe novel morphology for this species. According to an original phylogenetic analysis, based on a revised matrix of dental, cranio-mandibular and postcranial characters, Ls. maurettei is an early diverging lophiodontid morphologically close to Protomoropus and Paleomoropus, two basal chalicotheres, known from Asia and North America, respectively.
Since the authors omitted pertinent taxa and included irrelevant taxa, their analysis fails from the start.
“Our resulting topology does not support the previously proposed inclusion of the lophiodontids within the Ceratomorpha and supports a position within the suborder Ancylopoda, close to some Eomoropidae representatives. These results imply that Ls. maurettei was restricted to Southern Europe during the early Eocene, which would be compatible with an Asian origin for lophiodontids in accordance with the evolutionary history of other perissodactyls and placental mammals.”
The lesson here is the usual lesson: Don’t cherry pick your taxon list. Let a large gamut analysis tell you which taxa to test in your more focused studies.

References
Bai B, Wang Y-Q and Meng J 2018. The divergence and dispersal of early perissodactyls as evidenced by early Eocene equids from Asia. Nature Communications Biology 1:115 | DOI: 10.1038/s42003-018-0116-5 | http://www.nature.com/commsbio
Depéret C 1910. Etudes sur la famille des Lophiodontidés. Bull. Soc. géol. Fr., (4)10: 558-577.
Vautrin Q et al. (11 co-authors) 2020. New remains of Lophiaspis maurettei (Mammalia, Perissodactyla) from the Early Eocene of France and the implications for the origin of the Lophiodontidae. Journal of Vertebrate Paleontology. 40(6): e1878200.