Katarina and Zhonya's Hourglass
Solution 1:
Katarina's ultimate, Death Lotus is a channeled ability (as you may notice in the cast bar that appears and counts down). Like any other channeled ability, taking any other action, such as using an item like Zhonya's Hourglass, will interrupt the channel.
Other Champions, for instance, Fiddlesticks, Kennen, or Morganna, don't need to channel to maintain their ultimate, meaning Zhonya's can be used to safely shield them for its duration.