Lamb varies in age and size. American lamb tends to be harvested a bit older than Australian lamb. Size can vary due to age or breed. People's desires vary regarding how pink they like it. And also the texture they want from it. The instructions aim to cover most of the variables.
Even your idea of medium will vary from someone else's interpretation of it.
The time it takes for your rack to get up to temperature will depend on its thickness.
If you want medium with just a blush of pink, I'd probably be looking at 140F. I can't give you a time without knowing the dimensions of your rack, but there will be little difference in the outcome of the texture between the time it takes to bring the centre of the piece up to temperature and that done for 4 hours.