[T.G]

There's a little bit of truth in the original statements, but also a lot of what appears to be a misunderstanding of how the science works. Keeping a liquified gas cold will help prevent it from flashing to vapor, and also gases and liquids are more dense at colder temps, but none of this is going to create a situation of "there's more resistance to air creeping in.". If you could keep everything super cold, which might be difficult with the small mass of the lighter, you might get a smigeon more liquid in there by preventing flashing, that is if the can pressure is high enough, because as you cool the can, the pressure there is going to drop. So the reality is that you would actually want to cool the lighter and heat the can.

Honestly, I see it as a whole lot of work for very little return, and Adam brings up a good point about possibly damaging the lighter or it's seals by freezing it.