Your lap is the horizontal space, formed only when you sit, on the top of your legs between your knees and hips.
In context, to be "lapped" would mean to be seated on somebody's lap. For humans, this is a place that many children, especially children that are treated tenderly, spend a lot of time.
An "ample-lapped child" would be a child that gets to spend a lot of time sitting on a lap.
So, the poem is saying that, among other things, the person who is aged does not get to spend a lot of time sitting on some caring person's lap.