The basic idea is to use the formula for the distance between a point and a plane.

Let L1 have direction vector v1 and L2 have direction vector v2

And let P1 and P2 be the parallel planes containing L1 and L2 respectively

Then v1 x v2 will will be the Normal to P1.

Find a point on P1 and compute the equation of the plane P1.

Find a point on P2 and use the formula for the distance between a point and a plane.