The person who wrote the material in Valerie's link above was unsure of what the phrase actually meant, but just that it was used to silence over-inquisitive children. Certainly The Oxford English Dictionary has no entry for lay-holes.
Perhaps it's just another example of the sort of meaningless words for the same situation you will find by clicking here.
I had a notion that it might have originated in a mis-pronunciation, Andy, and actually had a look for le holes. Nothing there either, however. I like the 'leo' idea, though!