Your “mesh” appears to be a set of curves; not a Rhino mesh object which has vertices and straight lines connecting the
vertices. If the “mesh” is a set of curves it would be less confusing on the forum to refer to it as a curve network or similar.
Try the Patch command. A surface created using Patch may not lie “exactly” on the curves. Use Project or Pull to move the curves onto the surface. A similar question is discussed at Projecting surface to a Mesh