Background info in FFIV actually states that Cecil's dad was on the Blue Planet trying to speed up the process of human civilization reaching the Lunarians level.It's hinted that airship technology for instance was inspired by Lunarian influence in background materials. We also know this because we know the Tower of Babel and the Giant are Lunarian tech. As for their genetic compatibility, it could be similar to the Jurians in Tenchi Muyo! and that humans on the Blue Planet are simply a colonial world by the Lunarians that hasn't had enough time to develop back to their level, meaning they have a common ancestry.

I'm not sure I would say the Lufenians are a different race as much as the name of a culture that vanished thanks to Tiamat's influence. The title to me never sounded much like ''new race'' as much as it sounded like the name of their culture and civilization like say the Assyrians or Babylonians in our own history. Square is really big on the idea of advanced civilizations getting knocked back to the stone age by their hubris and needing to crawl back to that level thousands of years later. I think FFIX and IV are the only entries to avoid this trope since all the cool ancient tech from the past is actually connected to alien influence.

As for the Cetra/Human deal, that's also been hinted that they are in fact the same race, it's just that the Cetra keep to the old ways and retain abilities that humanity eventually lost. Course it's a bit fudged in the story because the script still contains some info from earlier drafts where the Cetra are an evolved race and chances are this is the narrative that Shin-Ra itself believes but figures like Bugenhagen show that humanity can also re-learn how to communicate with the planet. Course there is the debate about the possibility that the Cetra are just Spirains from another world and this is a FFIV scenario where human like races just conveniently evolve everywhere but that's a whole other mess.