You also mention no normal lift, but I bet there is storage on each floor to cover an old shaft from basement to roof.
Check the basement, bet you find trace of 4 to 6 more "roman baths". They are not !!
They are dye pits.
The one on the roof is probably adjacent to the old shaft, the laundry and a flat area which would have had lines across (for drying) in the old days.