(The best single source is Floyd S. Fierman’s article The Triangle and the Tetragrammaton, which appeared in several forms. The one I consulted was from the New Mexico Historical Quarterly, v. 37, n.4, pg. 310-323, 1962.)
Many of the stories revolve around Bishop Lamy’s relationship with the Jewish community in Santa Fe, in particular with Abraham Staab. Born in Germany in 1839, Staab had emigrated in 1854, eventually arriving in Santa Fe around 1857, where he established a trading and merchandising operation throughout the southwest. By the 1870s he was a prominent businessman and in the position to lend Lamy money for the Cathedral.
Fierman wrote that the most detailed account of Staab's connection to the symbol is from William Keleher’s The Fabulous Frontier. Keleher described how Staab had lent Lamy money for the Cathedral construction and how Staab said he would absolve all debts if he could chisel one word into the building’s entrance. Of course that word was Yahweh.
Keleher wrote that the source for his version was Staab’s son-in-law, who claimed that Staab had told this story on many occasions. In contrast, Fierman notes that Staab’s son Edward “avers under no circumstances” was there a trade of money for said carving. His father did destroy the notes, however, but “he did not bargain with the highest religious officer of the diocese.”