The problem again is taxon exclusion.
By following traditions and excluding so many pertinent taxa, Martinez et al. 2021 elevated an ordinary Late Triassic rhynchocephalian taxon into a headline.
Actually Taytalura (Fig. 1) is pretty much like two other taxa
we already knew about: Diphydontosaurus and Gephyrosaurus (Fig. 1), neither of which is at the base of the Lepidosauromorpha, nor that close to the origin of the Lepidosauriformes or Lepidosauria in the large reptile tree (LRT, 1915+ taxa).

From the Martinez et al. abstract
“The early evolution of diapsid reptiles is marked by a deep contrast between our knowledge of the origin and early evolution of archosauromorphs (crocodiles, avian and non-avian dinosaurs) to that of lepidosauromorphs (squamates (lizards, snakes) and sphenodontians (tuataras)).
Not true in the LRT where lepidosaurs are well represented by many more extant taxa than non-bird archosauromorphs. Martinez et al. must be referring to fossil taxa, but why omit either fossil or extant taxa when both can be and should be employed in a cladogram.
“Whereas the former include hundreds of fossil species across various lineages during the Triassic period1, the latter are represented by an extremely patchy early fossil record comprising only a handful of fragmentary fossils, most of which have uncertain phylogenetic affinities and are confined to Europe.
Affinities are resolved in the LRT. Europe does seem to be the center of early lepidosaurs, perhaps because that’s where so many lepidosaur paleontologists have been until recently.
“Here we report the discovery of a three-dimensionally preserved reptile skull, assigned as Taytalura alcoberi gen. et sp. nov., from the Late Triassic epoch of Argentina that is robustly inferred phylogenetically as the earliest evolving lepidosauromorph, using various data types and optimality criteria.
The authors are omitting Late Permian Lacertulus, Earliest Triassic Saurosternon, Late Permian Palaegama, Earliest Triassic Paliguana and other lepidosaurs in the LRT. The lepidosauriform, Tridentinosaurus is Earliest Permian (Fig. 2).

From the Martinez et al. abstract continued:
“Micro-computed tomography scans of this skull reveal details about the origin of the lepidosaurian skull from early diapsids, suggesting that several traits traditionally associated with sphenodontians in fact originated much earlier in lepidosauromorph evolution.
The authors don’t realize tetrapods with a diapsid skull architecture are not monophyletic, as the LRT recovered years ago (2013) by simplly adding taxa. Some diapsid-grade taxa are archosauromorphs. Others are lepidosauriformes. In other words, the archosauromorph, Petrolacosaurus is not related to the lepidosauromorph, Taytalura.
“Taytalura suggests that the strongly evolutionarily conserved skull architecture of sphenodontians represents the plesiomorphic condition for all lepidosaurs, that stem and crown lepidosaurs were contemporaries for at least ten million years during the Triassic, and that early lepidosauromorphs had a much broader geographical distribution than has previously been thought.”
According to results recovered by the LRT,
1. Taytalura has an abbreviated rostrum and a complete lower temporal bar. The plesiomorphic condition is a longer rostrum and no lower temporal bar.
2. Stem lepidosaurs go back at least to the Late Permian or perhaps the Early Permian (Fig. 2).
3. Broad distribution is probably correct given that Pangaea was a supercontinent in the Permian and Triassic.

Publicity from Sci-news.com
“A three-dimensionally preserved skull of a previously unknown Triassic-period reptile from Argentina illuminates the origin of lepidosauromorphs (lizards, snakes and tuataras).”
Not really. This skull nests basal to Diphyodontosaurus and Gephyrosaurus in the LRT, far from the origin of lepidosauromorphs (which includes turtles and amphibian-like reptiles in the LRT).
“The early evolution of lepidosauromorphs remains one of the largest knowledge gaps in reptile evolution.”
Not really. The LRT documents no gaps in the early evolution of lepidosauromorphs. Let’s try to make taxon exclusion a thing of the past. Colleagues: add taxa.
References
Martinez RN, Simoes TR, Sobral G and Apesteguia S 2021. A Triassic stem lepidosaur illuminates the origin of lizard-like reptiles. Nature https://doi.org/10.1038/s41586-021-03834-3