|You know it makes sense|
C.S. Lewis died before Star Trek was born. But he might have liked it (assuming he watched TV).
Lewis was a long-time fan of science fiction, and had been reading it when it was despised by most of the literati. He himself had experimented with Christian SF in his interplanetary trilogy, or at least the first one (Out of the Silent Planet)—the other two (Perelandra and That Hideous Strength) may be regarded as more fantasy. He was quite capable of enjoying writing that did not conform to his beliefs, and was deeply impressed by Arthur Clarke's Childhood's End.
What was really important to him in SF was myth. Both as a literary scholar and as a religious thinker he developed the concept of myth as story which conveys deep meaning, distinguishing it from other forms of narrative including allegory. Star Trek, at least when not reduced to the lower level of the "realistic", often provides a mythical quality.
Lewis commented that for imaginative people it was only the first journey to a planet that was of interest. One of his most magical visions is that of The Voyage of the Dawn Treader, the third of the Narnian books, where a small ship sails into the unknown, encountering marvels and terrors. This story has an underlying resemblance to the original vision of Star Trek: "to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before". As with the Enterprise, the story is not about conflicts between the explorers (once Eustace is reformed, anyway, and before that he was refusing the role of being one of the explorers). Conflict is provoked between them in one case by a deadly temptation they encounter, but it is not a conflict they brought with them.
The islands of The Voyage of the Dawn Treader correspond to the planets of Star Trek. In the Lone Islands the Narnians must overcome a problem which parallels real-world issues, and they do so with a Captain Kirk-like panache, but some other adventures are more mythical. Star Trek too covers both: compare "Let That Be Your Last Battlefield" and "The Alternative Factor". Lewis's voyage eventually reaches realities beyond the world, which Star Trek's travellers sometimes seek (e.g. Star Trek 5: The Final Frontier) but can never reach.
When Lewis died in 1963 he was not old. He was born in 1898 and had his health been better he would have been in his late 80s when TNG started. I can't quite imagine him in the poker game but he might have made a cameo appearance...