Strictly speaking no. The term ‘lacrosse’ was coined in 1637 by a French Jesuit missionary named Jean de Brébeuf who was watching some Iroquois play a tribal game. What he described, however, had very little in common with the sport played today. Games could last several days, were played on fields that could be several miles long (and wide), and some matches had teams numbering in the hundreds. The game was started by throwing the ball against the official’s head- an interesting choice considering the balls were large objects made of deerskin, clay, wood, and occasionally stone. The modern rules for the game weren’t applied till 1867 when a Canadian dentist named William George Beers founded the first official club and standardized the game.
So what’s the Byzantine connection? In the 5th century the emperor Theodosius II brought the game of ‘Tyzkanion’ to Constantinople. This unpronounceable sport was soon all the rage among the upper crust. It was played on horseback by two small teams of equal size each carrying a wooden stick with a net on the end. A small leather ball the size of an apple was placed at the center of a field and each team would have to scoop it up and throw it toward the opposing goal. Basil I was such a devotee that he built an official course on the grounds of the imperial palace and several emperors personally competed (one even died falling off his horse). In the 12th century visiting French Crusaders caught the tyzakanion fever and brought it back to France. They didn’t see the need for horses, so they modified it to be played on foot and changed the name to ‘chicane’. This slowly evolved into the game ‘la soule’ or ‘choule’ which French settlers brought with them to Canada. In 1867 William George Beers mixed the Native American and European sports and the modern game was born.
It’s not a straight line, but I think it’s fair to say that if lacrosse has an Iroquois mother, it may also have a Byzantine father.