Pipe runs for shower

We are installing a 1200 x 900 shower in the bathroom, next to the bath, into a 1360mm gap.

The back wall and the end wall are lath-&-plaster. What do you suggest regarding running the supply pipes? I think it would not be practicable to try to run them up inside the lath-&-plaster stud wall, as it probably has diagonal bracing. If one end of the tray is flush with the end of the bath, we could have 160mm gap at the other end between wall and tray – what do you suggest ?

This is not a duplicate posting. I have several different challenges for which I would appreciate advice.

160mm is more than enough gap, to erect a sort of false wall in which the pipes can be run.
2x2x should be adequate, and allow enough room for plasterboard/aquapanel and tiles.