There was no in-universe reasoning. Rowling thinks this is a plausible shape for scars.
When asked about the shape, Rowling said that she wanted something distinctive but still plausible.
I gave him a scar and in a prominent place so other people would recognize him. It is almost like being the chosen one, or the cursed one, in a sense. Someone tried to kill him; that's how he got it.
I chose the lightning bolt because it was the most plausible shape for a distinctive scar. As you know, the scar has certain powers, and it gives Harry warnings. I can't say more than that, but there is more to say.
Bolger, Kaitlin and J.T. Sprague. "J.K. Rowling answers a few kid questions," Houston Chronicle (conference call), March 20, 2001.
I interpret this to mean that in-universe it was just a scar and therefore kept to the shape that a plausible scar could keep to. Out-of-universe, Rowling picked the most distinct shape she thought could happen from a scar, in order that Harry would be recognized by it. But there was no in-universe reason for the shape.
It's worth noting that the original Pottermore developers had toyed with the idea of showing the avada kedavra wand movement to be in this same shape, presumably implying that the scar followed the wand movement, however this never actually ended up being used on Pottermore, and so may have never been approved. In any event there's no linkage of the idea to JK Rowling.