I'm definitely not informed enough on the history of lacrosse as an organized sport among prep schools and colleges, however, the modern game originates with William George Beers, who is often credited as being the "Father of Modern Lacrosse" for establishing the first set rules of lacrosse in 1857.

I remember reading that early on, Canadian teams would play Haudenosaunee teams, mostly the Mohawks of Kahnawake near Quebec, and would get absolutely demolished, due to the modern game's style being based off of the Haudenosaunee style of the game (Many indigenous nations played a form of the game and has distinct names and various purposes culturally, the Haudenosaunee form is the one that just became popular.) It wasn't too long after that, "Iroquois" teams were banned from playing against Canadian teams because they were considered professionals. I believe I also read elsewhere, teams could be allowed to have 1 Iroquois player on their rosters to level the playing field, so to speak.

So right off the bat, modern lacrosse isn't off to a good start with inclusion, especially of the people with which the game originates. This new sport was considered a "gentleman's sport", further adding to the affluent nature the game would take on.

If I can take an educated guess as to why the game was really mostly played by prep schools and colleges? Cost, availability, and accessibility of equipment, particularly that of the lacrosse stick itself.

In the early days, the best quality sticks were being produced by Mohawks at Akwesasne. The process to make a wooden lacrosse stick of good quality takes anywhere from 6 months to a year from harvest, to steam beanding, curing, and carving and stringing. Frank Lally started the Lally Lacrosse Manufacturing Co. which employed all Mohawk workers at Akwesasne, and operated from the 1880s until WWII. I read that it was estimated ~90% of all lacrosse sticks during this period were produced at Akwesasne, mostly Lally's, and used throughout Canada, England, and the US.

What's interesting during this period as well is how rapidly stick technology evolved. The rules of lacrosse changed often, and thus the dimensions of sticks as well. Old lacrosse sticks from the late 1800's were often referred to as "long-frames" because of the long head area and short shaft (hah). Towards the 1930's, the head area becomes shorter and shaft longer. Box lacrosse, an indoor variant of the game played during the summer months to fill hockey arenas which would typically be vacant, also becomes popular in Canada at this time. Because of the narrower quarters, sticks in this game also evolve to be shorter and narrower in their frames to control the ball better.

So 2 styles of Lacrosse, Box and Field, played with different stick types, are being played by affluent people for the most part. Keep in mind, to be able to buy sticks and equipment in bulk to field a whole team, you had to have some money to shell out. It's far more accessible and cheaper to play football or baseball or any other sport if you don't have the means.

In the 1970's, the Mohawk Lacrosse Manufacturing Company factory burned down, halting wooden lacrosse stick production and distribution worldwide. Additionally, quality hickory trees used to create sticks were getting harder to source. In just a few short years, plastic heads with metal shafts began being produced by non-natives out of necessity, and it's been the standard since. One would think making sticks of easier to obtain materials would decrease the cost. Quite the opposite. Despite innovation in these sticks' quality and ability to produce them in larger volumes to meet demand, prices have only increased to today.

It's lacrosse's biggest barrier of entry; Cost. Helmet, pads, stick, and cleats, can run about $800+ with high end equipment. And then there's club fees, tournament fees, etc. Thousands more added on yearly. It's no wonder the game is not more popular. I will add that there are growing efforts to make the game more affordable not just here in the US, but also around the globe. There's also conscious efforts now to acknowledge the Indigenous roots of the game and rebranding the image of lacrosse away from prep school or frat boy culture, places of extreme privilege. But it will take more time and effort to work toward acessibility beyond those places.

One last thing I'll leave here; The early Iroquois teams that were banned from playing early on, what did they do? Well, they played each other. Mohawk reserves had enough men to field multiple teams, likewise at Six Nations Reserve. In NY, Onondaga, Newtown, and Tonawanda played among themselves and remain to this day some of the best players in the world against strong contenders like the US and Canada, places that tried to exclude them from a game that they've always played. The Haudenosaunee Nationals men's lacrosse team is ranked third in the world internationally among 79 countries.

Hopefully this long-winded answer gives a little perspective of lacrosse's history and it's changing image today.

While you wait, please see this answer, from a Canadian perspective, by u/candidate0: https://www.reddit.com/r/AskHistorians/comments/6mbr3m/how_did_lacrosse_come_to_be_adopted_as_a_college/

u/foreverandafew's great response gets into the history of the sport and I want to catch the ball they threw (really weak lacrosse pun there) and get into some of the reasons it's so strongly associated with private schools and colleges.

The first thing I would offer is a slight correction. That is, generally speaking, the game is is more likely^1 to be found played in schools and colleges that are predominantly white and upper-class communities, including public school districts. To understand why that is, it's helpful to step back and look at the purpose private high schools and colleges serve.

Until a sea change in the late-1800s as school increasingly became something all children did - regardless of class or race - the main focus of formal education was a "classical education" or "classic curriculum." Students (mostly boys, mostly white, mostly non-disabled) worked to learn the things that smart men knew. Greek, Latin, some math, some sciences, rhetoric, logic - that kind of stuff. In other words, formal academic education wasn't meant to be practical. It was meant to prepare a young man to be able to discuss issues of politics, economics, religion, and whatever it was that a room full of men with access to power would discuss and recognize the historical, literacy, or religious references their conversations would contain. I'm streamlining a bunch of history related to early American education but it's safe to say the goal was exclusivity.

As formal education spread and the primary, secondary, and tertiary system took shape, there was a clear desire among men with access to power to maintain that sense and structure of exclusivity. Feeder schools, such as Boston Latin, maintained or established relationships with the Colonial Colleges (many of which are members of the Ivy League - more on that overlap and the idea of prestige here.) As Catholic immigrants arrived in large numbers, especially in large cities like New York City, Protestant families with access to political power and financial resources fought to maintain religious education in public schools, forcing a schism in American education that gave rise to the parochial school system, dominated by private Catholic schools. Meanwhile, for some families, the presence of immigrant children from lower social classes lead to them establishing or cultivating private secular schools that carried on the "classical" education traditions. Eventually, as schoolhouses consolidated into districts and districts hardened their boundaries, white parents shifted their power to the suburbs, creating enclaves of well-resourced, low-need, suburban school districts with lots of space for playing fields and discretionary income available for supporting a child's sporting adventures.

If we cycle back to that idea of connections, exclusivity, and privilege that was a key component of early American education, we can trace them forward to today's enclaves of white families where formal education is seen as a means of maintaining power. Lacrosse fits neatly into that worldview as it was one of the sports that was popular among men with access to power - along with sports like polo, yachting, trap shooting, and cycling. (All of these sports were listed in the weekly "Sports and Sportsmen" column in the New York Tribune, along with the names of clubs where one could play. I checked into the history of a few of the clubs and they were all founded by "Yale Men" or "Harvard Men", etc. etc.)

Donald Fisher, in his 2002 book Lacrosse: A History of the Game links political and economic relationships between New England men with access to power with Canadian men with access to power as one of the main drivers for making the game a marker of wealth and exclusivity. While the game was played across the region before Beers established the rules as explained by u/foreverandafew, once white men began playing it in their clubs, it made sense for their sons to learn to play as well. In terms of why lacrosse appealed to men with access to power, we can be fairly certain that it's roots among Indigenous nations was part of its appeal. In a previous question, I got into why so many schools adopted mascots based on Native imaginary, and get into the idea of Americana. In that answer, I quoted some of /u/Georgy_K_Zhukov's writing on the topic and I think their words are applicable here:

So in short, the [mascot] was never a celebration of the Native American as who they were, but what the idea of 'Indian' was to white people. Whether that was as a symbol of white liberty in the mid-19th century, or adding on idea of white masculinity in the early 20th, the specific design could change but it continued to reflect white ideas and white attitudes; ideas of nativist liberties, or ideas of a national myth, one which was now part of history and not the present, a place where white America had spent the past few centuries doing their best to consign the real people whose images they continued to parade, both about and in.

So, to sum up, lacrosse became strongly associated with a particular kind of private schools and colleges in the US because white men with access to power claimed the game as a marker of their class, race, and gender and created structures for their sons to play it.

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1.The Inside Lacrosse High School Rankings now distinguish between private and public schools and a quick review of the public high school rankings speaks to how many of the schools are predominantly white, well-resourced, low need suburban school districts. That said, there are number of teams at low-resource, high-need districts, many of which are located on or near Native nations and/or reservations.

This isn't a direct answer to your question, but it's worth noting that the Iroquois Confederacy is still a powerhouse of lacrosse. It's an important part of their culture. Lyle Thompson, for example, is considered one of the sport's greatest players.

He took some shit about his long hair a few years ago... I guess it's still too difficult for some people to grasp that it's ok for people to be different. Here's what he said:

My hair is more than just my identity. It’s more than just showing everyone around the world who I am, that I’m Native American. It brought back memories, things we do, traditions I’ve done with my hair since I was a kid.