Lanthanolania and Saurosternon nest at the base of the Lepidosauriformes, defined by Gauthier, deQuieroz and Estes (1988) as Sphenodon and squamates and all organisms sharing a more recent common ancestor than they do with younginiforms. They intended this to include Paliguana, Saurosternon, Kuehneosauridae, Rhynchocephalia and Squamates, but in the context of the present study their Lepidosauriformes would be redundant with the current Lepidosauromorpha.
Redefined, the Lepidosauriformes now includes Paliguana, Sphenodon, their most recent common ancestor and all of its descendants.
That now includes rhynchosaurs, trilophosaurs and pterosaurs which were formerly excluded.
Between Paliguana and the Lepidosauria the present cladogram looks very much like the one presented by Gauthier, deQuieroz and Estes (1988). They considered the Younginiformes to be ancestral, but that clade is unrelated according to the present larger study.