I just assumed that Big Town sent their kids there.![]()
That and I'm assuming something slightly darker as well. Something like some couple has a child that they realize they can't take care of for whatever reason so they abandon the child at this rumored place they've heard of called Little Lamplight. If I remember right, Little Lamplight is on the route for the trade caravans, so its existence must be known to the wider wasteland.
Which opens up another possibility: any orphans the traders find on the road probably get left at Little Lamplight the next time that caravan stops there.