Symbolism, Imagery, Allegory
Here's a list of the items Childan sells or tries to sell at his American antiques store: Civil War pistols, Civil War recruiting poster, and a Mickey Mouse watch.
There's other Americana that Childan mentions, from a butter churn (ooh) to a framed picture of Jean Harlow (aah). But the items he does sell (or almost sells) includes quite a few Civil War antiques. That makes some sense: in a book about a torn-apart U.S., we hear a lot about antiques from an era when the U.S. was torn apart. For extra irony, try this: these items that were associated with the near-end of the US have come to be symbols of American identity.
And then we learn that some of these antiques are more like "antiques." We never know how many of Childan's antiques are actually clever forgeries, which definitely connects these antiques to issues of deceit and uncertainty. Add to that the fact that some of these fakes are made by "Frank Frink," who is himself kind of a fake, since he changed his name and nose to survive. (It's like the paper writes itself.)
Now, Childan doesn't know about his "antiques," but Wyndam-Matson clearly knows, since many of them come from his store. W-M has his own idea about authenticity and historicity, which is that it's all in the eye of the beholder. So for him, fakes are as real as authentic antiques as long as the person thinks it's real. And he has proof: two lighters that look identical, though only one was in FDR's pocket when he was assassinated (5.26). Or, as he says, the whole idea of historicity is "all a fake, a mass delusion" (5.30). So Childan panics about the fakes, but for W-M, faking identity is as good as having a real identity.
Alternate Symbolism (Just for You)
We're considering this lighter in terms of history and authenticity. But if you wanted to, you could connect it to issues of creating a better world and surviving in this Nazi-triumphant world. That FDR lighter was present at a critical moment, when the world took turn for the worse.
In this new world, as Frank Frink notes, Nazi-style barbarism could even imagine dehumanizing Africans to the point of using their bodies for products—for instance, lighters: "Ja, Herr Doktor. A new use for the big toe; see, one can adapt the joint for a quick-acting cigarette lighter mechanism. Now, if only Herr Krupp can produce it in quantity" (1.61). So lighters could be a symbol of the evil in this world.
But that doesn't mean that lighters are always associated with badness. As Childan notes, the bad and good are connected, that light comes out of darkness according to Japanese philosophy (7.24). So out of the potentially negative—lighters—we have a potential positive: cigarettes. Or rather, we have the fake cigarettes that Baynes uses to pass secret information to Tedeki (12.80). And it's this information that might end up making a better world. So FDR's lighter was present when the world took a turn for the worse, and Baynes's cigarettes were present when the world (hopefully) took a turn for the better.