Take a 3D set of Cartesian coordinates. Imagine a unit cube with one vertex at the origin (0,0,0). The base of the cube has two edges, one lying along the x axis and the other along the z axis. A vertical edge lies along the y axis. In the x-y plane graph y=x. Part of this line is a diagonal of one face of the cube.
In the x-z plane plot x+z=1. This is a base diagonal which doesn't pass through the origin, so it doesn't intersect y=x in the x-y plane,
In the plane z=1 plot x+y=1. This is a diagonal of the face parallel to the x-y plane. It doesn't pass through the origin or any vertex on either of the other two lines.
So we have three non-parallel, non-intersecting, non-coplanar lines as an example.