As this is a special case, the FIL/IWGA came to a special agreement.
The Gods of the Haudenosanee (Iroquois) people gifted the sport of Lacrosse to them. In turn, the Haudenosanee gifted the game to the rest of the world. The Haudenosanee are the spiritual keepers of the sport, much the same way as Scotland is with Curling, Japan with Judo, and Korea with Taekwondo.
Recapping the posts from above: The Haudenosanee were originally not invited to the World Games, since they do not have an NOC. Their players then created a petition asking the other nations to boycott the Games, which received wide support in the Lacrosse community. The IWGA/FIL then decided that the Haudenosanee could compete if they had met the qualification requirements (which they easily had), as this was a special case. Ireland the decided (voluntarily) to reject their place at the Games, so the Haudenosanee could compete.