Safe in a cave? Not always.
I recall reading an account in Accidents in American Mountaineering years ago of a small party of climbers who took shelter in what amounted to a "cave" (probably an overhang on the mountainside) during an electrical storm.
The groundspike flowed down the mountainside, arced across the open air of the "cave" and rgrounded through several climbers on its way down the mountain. The climbers were probably not very deep inside the "cave" but it was the only shelter available. Now if the cave had been 100 feet in length, maybe the groundspike wouldnt have reached them. Speculation only.
All one can do when caught in a lightning event is reduce your risk of strike. I doubt that there is any way to totally eliminate it.
Jim
And I like the MythBusters idea!