At what distance is lightning dangerous for someone lying down? My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but it looks like that there is no better or worse position.
I then tried to find some information on the actual risk of lying down, but found none. I can imagine a worst case scenario where the lightning hits you close to your feet so that you are radially oriented towards the field change and that the potential difference between heart and feet would be enough to trigger a ~30+ mA current in your body (this is also the limit for AC current in home installations in Europe).
Assuming that you are not fried (and whatever is practical for the estimation), would the radial potential gradient big enough for a lethal current?
 A: This is often referred to as the "step voltage". The image below illustrates the electric field. (it's caused by a wire and not by a lightning, but you get the idea)

from here: http://commons.wikimedia.org/wiki/File:Potenzialtrichter_Freileitung.svg
The problem of touching two points of the ground is that there can be a difference in the potential of the field, in other words: voltage. Given that and the resistance of your body the result is current and possibly death.
How big the voltage is depends on the difference of how far the two feet are apart.
Both approaches that you mention minimize that distance.
Crouching will make you more upright and thus more prone to being hit by a lightning. 
I personally would never lay flat on the ground unless I was in a vast empty area where reducing the risk of being fried directly is the top priority.
In any other situation, lying flat on the ground seems to be an inferior approach to survival. Considering a very dangerous situation, you are actually expecting a lighting strike. And that can very well hit that tree over there. And if there's a burning tree falling towards me, I'd rather be in a crouching position than lying flat on the ground in order to run for my life.
But keep in mind that being knowledgeable about that stuff doesn't change the odds in your favor:

image from here: https://xkcd.com/795/
