Buying print books on Amazon
How do Lulu print books ordered on Amazon get printed by Lulu?
Print on Demand
On Amazon, they are printed by CreateSpace/KDP, who Amazon own. Lulu do not actually print any books. On sites that don't use their own printshops (which is most of them) an order will be printed by one of Lulu's approved printers, and as close as possible to the buyer's address.
It's all processed by very clever linked software
All that matters is that when one of our books is sold, anywhere, our share of the payment is sent to Lulu.