So! The sentence I once had the urge to write -- "There is zero evidence of any archosaur giving live birth..." would urgently need editing for style, but is essentially correct?
It is correct.We don't know the mode of reproduction of the metriorhynchids, though. They converged pretty heavily on ichthyosaurs (feeding mechanics and thus skull shape mostly excepted).
There are, in fact, some live-bearing geckos (one species in Rhacodactylus, and some in Hoplodactylus; perhaps others).
ARGH! Sorry! Yes, there are -- but hard eggshells are restricted to a clade within Gekkota, and the live-bearing ones are all outside that clade, AFAIK.