LaCrosse is of course, derived from the French word for Cross, 'Crosse,' and the sport is one of Canada's National Games, the other being Hockey. The French thought that the game's signature stick resembled a Bishop's Crozier, or cross.
It was first recorded by Jean de Brebeuf in 1683, in what is now Southern Ontario. The Indigenous peoples that played this game had their own name(s) for it, but the French name stuck amongst the non-Indigenous settlers. It was played amongst the First Nations as a game for the Creator, and had cultural and Spiritual significance, as well as being a method of settling disputes, despite popular belief.
Early on, the sport was popular and games between the townsfolk and the First Nations peoples were common, although it is said that it was many years before any significant wins were logged against the Indigenous teams. It became popular in places like Montreal, and by the 1850s was a popular sport in many cities. It was declared Canada's National Game in 1859.*
*Source: Mike Mitchell, Director, North American Indian Travelling College