The first thing that came to my mind was a keypad or a touch panel to enter the number of floors. But, I suppose 1000 floors' lift will be so crowded that an individual will hardly get enough space around keypads to enter the number of their floors. Yes, you can multiple keypads at several places, but I think I also prefer an idea of a Siri interacting with me.
I would also assume that there will be multiple lifts to reach 1000 floors. In that case, an individual can enter their preferred location in the lift lobby and lifts can be prioritized to take people to their respective floors at the earliest. Or different lifts for different floor ranges.
I might also think about an app for this 1000 floor lift, where I can enter my floor number and may be passwords for private floor access.
But there are many questions that pop-up before you think about designing it, like who will be using it, which floors it will stop, whether it's residential or commercial and much more, these questions will be determining for the UX.
thanks @dougcollins for posting it, it will be interesting to see different opinions on it.