The French Jesuit missionary, Jean de Brébeuf, saw Iroquois tribesmen play it in 1637 and was the first European to write about the game.[6] He called it lacrosse. Some say the name originated from the French term for field hockey, le jeu de la crosse.[7] Others suggest that it was named after the crosier, a staff carried by bishops

However the famous George Catlin watercolor of “Ball-play of the Choctaw–ball up” circa 1834-1835. Depicting my great-grandmothers tribe is perhaps the most famous early depiction of the sport. n. b. Choctaws where native to Alabama-Mississippi area; later to be forcibly removed by old dick head Old Hickory Andrew Jackson. Therefore the game is prevalent in the North Americas. . . hardly obscure and hardly strictly Canadian.

Lifted from Wikipedia except as noted and comments about Choctaws and dickhead.

“When French explorers were first introduced to the native ball and stick game, baggataway, they called it ‘la crosse’ for the stick’s resemblance to a bishop’s crosier. Europeans began playing the game in the 19th century, but rules were not standardized until lacrosse goalkeeper George W. Beers published the first set in Montreal in 1867. In 1994, lacrosse was declared the national summer sport of Canada.”

BTW, Americans can be credited for spreading the sport to Japan. I highly recommend the lacrosse / martial arts film, “Shaolin Girl.”