Hello - try:
Make a vertical line of the same height through the center of the cube. Loft one of the angled lines to the center and ArrayPolar the loft surface. Intersect the surfaces and the cube.
create your “cube” with _loft of two curves.
use option SplitAtTangents = No
(or other workflows to get a single surface)
_unrollSrfUV
(check this forum for Info on developable surfaces)
construct / draw the lines in 2d on the unrolled surface.
_flowAlongSrf
to map them back to the “cube”
(also check for _flowAlongSrf there are a few aspects to care of)