I have a player who is currently an afflicted lycanthrope, meaning he has contracted the curse of lycanthropy. He wants to eventually become undead (specifically, a mummy) and I know undead are immune to disease, but as lycanthropy is considered a contracted curse and not a contracted disease I am wondering if his lycanthrope template would remain or fall off.
So by the rules, lycanthropy is neither a curse nor a disease; it’s a template. The “curse of lycanthropy” is really a curse that causes you to gain the template—the point being, once the template is applied, the curse isn’t really a part of the equation. Similarly, for all lycanthropy spreads “like” a disease, it isn’t one. This is why the curing lycanthropy section needs all these special rules for handling it—it isn’t your standard curse or disease. The spells break enchantment, heal, remove curse, and remove disease don’t normally do anything to a template, hence that section.
The section does not, however, address immunity. The template itself kind-of addresses the concern when creating a lycanthrope in the first place:
“Lycanthrope” is a template that can be added to any humanoid or giant (referred to hereafter as the base creature).
But templates are not removed if the creature would later become ineligible to receive them (indeed, many templates make changes to the creature that would invalidate themselves, so it would be a problem if they did). So while an undead creature is not allowed to become a lycanthrope (they have the undead type, not the humanoid or giant type), a lycanthrope could become undead—and nowhere is this mentioned as ending the lycanthropy.
Now, in your world, you could reasonably rule that lycanthropy is enough “like a disease” to not apply to the undead, or that it is otherwise incompatible with lycanthropy. But you could also very justifiably rule the opposite way, and that ruling is more consistent with the rules, both in their technicalities and also (I would argue) in their spirit.