Laying them up and picking them down
This phrase is appeared for the second time in the story:

So, in the story the boys are still walking unable to stop...
"I don't want to do it anymore," Olson said hollowly. "I'm sick of it."
"Raring to rip," McVries said turning on him. "Isn't that what you said? Fuck it then. Why don't you just fall down and lie then?"
"Leave him alone, let him do it his own way" Garraty said.
Olson didn't say anything. He just kept picking them up and laying them down.

What does it mean?

Question

Laying them up and picking them down
This phrase is appeared for the second time in the story:

So, in the story the boys are still walking unable to stop...
"I don't want to do it anymore," Olson said hollowly. "I'm sick of it."
"Raring to rip," McVries said turning on him. "Isn't that what you said? Fuck it then. Why don't you just fall down and lie then?"
"Leave him alone, let him do it his own way" Garraty said.
Olson didn't say anything. He just kept picking them up and laying them down.

What does it mean?

Answer

If "Laying them up and picking them down" is what appears in your book, then it is probably a play on "Picking them up and laying them down". The meaning may become more apparent as you continue the chapter. I don't know the meaning from what you posted. Sometimes writers play with words like that.

Answer

Well, your title is wrong. The phrase is:

Picking them up and laying them down.

So what is your actual question?

Answer

In this context the phrase means "they mechanically kept going", "they kept dragging their feet"

Hope it helps ;)

Answer

"...the boys are still walking, unable to stop."
"He just kept picking them up and putting them down" - refers to his feet.