Is this a new home in design or existing? Also, where is this (US, UK, EU?)

Generally speaking for the US, work like this on a three story home will require a permit and a licensed design professional whether it is a new design or (especially if) it is in an existing home. Aside from the mechanics and safety aspects of the product itself, you need to deal with the fact that to install it you are creating a three story fire passage and that needs to be done carefully and correctly. It may be that lift manufacturers will have all the design aspects covered with respect to their product, but they probably won't be well geared to help you re-arrange your interiors to accommodate the shaft in a well-planned and code compliant way. For that you'd want at the least an interior designer, but ideally an Architect to help you sort it out, and in the US, most states will require a licensed design professional.

So... the short answer to the long explanation above, is head straight to a local licensed design professional for advice as soon in the process as you can. They can help you sort all this out in the best way for you.

100% behind ReSquare (I'm in Europe)

It is an existing structure in the US.

In the US, I'd recommend you consult a local Architect. An Architect is qualified to sort out all the issues involved for you.