There are other approaches to 2-D lifts. ThyssenKrupp are promoting one using linear motors (look mum no wires!), which they have been demonstrating in their test tower in Rottweil*. There's
a video of that too, which shows it working (and there's more in their sales material online too). I'm not convinced by that as a solution - it just looks wrong, somehow. No doubt other makers are also working on similar ideas - and in the case of Kone, their test facility goes the other way: it's in an old mine shaft.
*Yes, of course it's where Rottweilers come from.