Nothing directly prevents it.
The key question here is about who can be affected by different curses.
The Monster Manual (p.206) says:
Curse of Lycanthropy. A humanoid creature can be afflicted with the curse of lycanthropy after being wounded by a lycanthrope...
For an NPC, it's inarguable: A lycanthrope (afflicted or not) is a humanoid (shapechanger). The "Player Characters as Lycanthropes" sidebar states that you get the nonhumanoid form's speeds, immunities, traits, and actions that don't involve equipment, but it doesn't mention gaining the shapechanger tag, though I assume the intent is that you do become a shapechanger. That doesn't actually do much, though; you're still a humanoid.
The Vampire stat block (p.297) says:
Bite. [...] A humanoid slain in this way and then buried in the ground rises the following night as a vampire spawn under the vampire's control.
So a vampire spawn is an undead, which is not a valid target for the curse of lycanthropy. But does that matter?
The curse of lycanthropy can only be passed to a humanoid, but it doesn't seem to go away or break if the creature type changes to undead later, and nothing says the curse is removed when its target dies, so there seems no rules-as-written reason to say that dying and rising as a vampire would break the curse. It might be mechanically unwieldy to have so many extra traits and actions on a creature, but it doesn't seem technically problematic.
That said, as DM you could certainly decide that there's a reason the two states can't coexist, or that the vampire's Shapechange ability replaces the Lycanthrope's Shapechange, making the hybrid and animal forms inaccessible even if they're still technically a lycanthrope. I don't see anything off-hand that would be totally broken about a vampiric lycanthrope, you just need some fairly specific weaponry to fight them.
So far as I can see, there's nothing that stops you from having a ghost werewolf, vampire werewolf, or zombie werewolf in your game. Whether the ability to spread the lycanthropic curse remains in their undead form, I can't say. In theory it does, but feel free to do what you want to do.