What is the source of these "Lay Bodhisattva Vows"?
Okay I found the answer. 

It's from the "Sūtra of the Upāsaka Precepts" (Shansheng Jing). It was translated into Chinese in the 5th century. 

http://www.sutrasmantras.info/sutra33c.html

This sutra has similarities to the older Sigalovada Sutta http://www.accesstoinsight.org/tipitaka/dn/dn.31.0.ksw0.html

(Ref comparing the UPS and Sigalovada: "Buddhism and Peace", chapter 10)