The questions being asked are themselves tricky, falling under the umbrella of what was discussed before. Indeed, the entire subject of what was around the mouths of extinct sauropsids and even basal therapsids is an open question, involving various conditions of the Extant Phylogenetic Bracket, the "null" hypothesis and how we reconstruct that, degrees of inference based on half-understood conditions of bone texture, microstructure, Sharpey's fibres, and natural preservation and what is found/inferred from that. And of course, the "common sense" that gave rise to arguments such as the necessity of an oral seal, and so forth.
But there are some ... speculations. I'd rather not invest too much time in them here. I already talked about Ichthyornis (in connection to Hesperornis)
here, and the reasons why I reconstruct it with a half-beak/half-lip, but that's really just scraping the tip of the research which is further referenced throughout the body of work being talked about in this thread (not anything to do with me, mind you).
Of particular note here, is the nature of inference (a logical argument, not a scientific one; although they should align they don't always) and the null. The null is the basic argument from which all things spring, the natural assumption based on various preferred or observed conditions. "All birds have beaks" is a null, because there is no contradiction in extant taxa. To infer that things such as the spikes on pelagornithid beaks are "teeth" requires extraordinary evidence which has been lacking, but was discussed at one time or another; so we revert to the null, and assume, from the beginning, that the argument is "if the spikes are part of the beak, then..." We also get into a bit of begging, but that's how these things go.
As a result, we can only really speculate from what we see: fish, amphibians, various of them, mammals, squamates, turtles, crocs, and of course, birds. All of these tetrapod and outlier groups give us the various constraints upon which we depend, and from them (or because of them) we are required to use them as the models for our extinct taxa, some far removed in morphology from their origin. Classically, it's "if crocs don't have lips, and birds don't have lips, do dinosaurs?" Or, "if turtles don't have lips, but snakes and lizards have lips, then do ichthyosaurs?" Or, "if teeth desiccate while not inundated with water (we're begging here, pardon me) then do pterosaurs have some method of preventing this when their teeth are always exposed?" Consider long-tooth flying foragers such as many anhanguerids and rhamphorhynchids. They would spend most of their time out of the water, so the aerial exposure to their teeth must be great. So... do they desiccate?
These we want to know before we can reasonably answer questions like "do dinosaurs really have lips?" with such certainty that all of paleontology follows along. We're getting there, and the concensus is, it seems to me, falling that way among opinions. But facts? Slightly behind.
Anyways, I hope this helps.