Since the planet's "spin" has little to do with magnetic polarity if the planet's core is set up a certain way, is it possible that the magnetic polarity axis is (almost?) perpendicular to the rotational axis? So it's basically Earth but with a magnetic alignment such that all compasses point to Greenwich or Utah or whatever.
[EDIT]
Oh, erm, you were saying that Luthadel was the AXIAL pole. Well, that could still work... sort of. What we think of as an Earth year is really the time it takes for our planet to make one revolution around the sun, and an Earth day is the time it takes for Earth to make approximately one rotation on its own axis (I say approximately because each time a day goes by the Earth has also moved slightly, so since I'm too lazy to figure out what it is I'm gonna say give or take a few minutes because the day is subjectively defined, and a period of 24 hours is the amount of time it takes for the sun to appear to be in roughly the same location in the sky to someone standing in roughly the same location on the ground).
If that confused you, don't worry. It's not that relevant. I just brought it up because I'm insane. God told me to.
So. We know now that some planets have shorter years than days. But since a year also changes the observed location of the sun (if we had substantially less than 365.22 days each year, we'd probably notice more), such a planet would count its years as "days" and its days as "years."
So if the planet Luthadel is on (I forget which page Brandon named the planet on) happens to revolve around the sun more than 100 times faster than it actually spins (this is definitely scientifically possible because it has been observed), Luthadel could still have days and nights as long as its axial tilt wasn't perfectly parallel to its revolution axis.
In fact, suppose the axial tilt is perpendicular to its revolution axis. That is, suppose Luthadel is actually on the north "pole" of the rotational axis, but it is also simultaneously on its equator (like Uranus, though Uranus isn't perfectly perpendicular either). This would make for "days" of exactly the same length in Luthadel. Of course, this would make for a strange time system -- a "year" would vary depending on where on the planet you were; Luthadel itself wouldn't actually have seasons in this scenario (but a slight tilt from this would allow for seasons), and the further you got from Luthadel the more volatile the seasons would get, until you started approaching the south pole.