I analyzed the polyphyletic origin of glycyl-tRNA synthetase (GlyRS) and lysyl-tRNA synthetase (LysRS), making plausible the following implications. The fact that the genetic code needed to evolve aminoacyl-tRNA synthetases (ARSs) only very late would be in perfect agreement with a late origin, in the main phyletic lineages, of both GlyRS and LysRS. Indeed, as suggested by the coevolution theory, since the genetic code was structured by biosynthetic relationships between amino acids and as these occurred on tRNA-like molecules which were evidently already loaded with amino acids during its structuring, this made possible a late origin of ARSs. All this corroborates the coevolution theory of the origin of the genetic code to the detriment of theories which would instead predict an early intervention of the action of ARSs in organizing the genetic code. Furthermore, the assembly of the GlyRS and LysRS protein domains in main phyletic lineages is itself at least evidence of the possibility that ancestral genes were assembled using pieces of genetic material that coded these protein domains. This is in accordance with the exon theory of genes which postulates that ancestral exons coded for protein domains or modules that were assembled to form the first genes. This theory is exemplified precisely in the evolution of both GlyRS and LysRS which occurred through the assembly of protein domains in the main phyletic lineages, as analyzed here. Furthermore, this late assembly of protein domains of these proteins into the two main phyletic lineages, i.e. a polyphyletic origin of both GlyRS and LysRS, appears to corroborate the progenote evolutionary stage for both LUCA and at least the first part of the evolutionary stages of the ancestor of bacteria and that of archaea. Indeed, this polyphyletic origin would imply that the genetic code was still evolving because at least two ARSs, i.e. proteins that make the genetic code possible today, were still evolving. This would imply that the evolutionary stages involved were characterized not by cells but by protocells, that is, by progenotes because this is precisely the definition of a progenote. This conclusion would be strengthened by the observation that both GlyRS and LysRS originating in the phyletic lineages leading to bacteria and archaea, would demonstrate that, more generally, proteins were most likely still in rapid and progressive evolution. Namely, a polyphyletic origin of proteins which would qualify at least the initial phase of the evolutionary stage of the ancestor of bacteria and that of archaea as stages belonging to the progenote.