If Ezreal or Lux get CC'd during their ult channels...

It's actually just a very long cast animation, not a channel. They work similarly to how Garen's spin, Viktor's Death Ray, Corki's Gatling, etc don't stop no matter what CC happens to the champ while the effect is active (Lulu's Polymorph is a rather silly application of this - Squirrels with Garen's spin particles, but without the actual spinning animation...).

That said, Death is the best CC for things like this.