So, it sounds like you want to start your trip in Richmond, drive through part of Shenandoah NP on Skyline Drive, visit Luray Caverns and then continue to Lancaster, PA (not Lancaster, VA , I assume).
If I were making this trip, I would drive from Richmond and enter SNP at the Swift Run Gap entrance. (You'd drive on I-64 to Rt. 15 to Rt. 33). Drive up Skyline Drive and exit the park at Thornton Gap on Rt. 211 to Luray. From Luray, you have many options on routes to Lancaster. I'd probably choose Rt. 340 to Harper's Ferry, Rt. 15 to Gettysburg and then Rt. 30 to Lancaster. It should be a scenic drive in many places.