Looking at the different ways colonisation occurred in what became India and Canada may help to answer your question.

Qualifier: this is an extremely generalised answer.

In the 1780's, in Calcutta, a group of British 'gentlemen' formed the Marylebone Cricket Club. Cricket was a sport played by gentlemen in Britian, that is Earls, Dukes, etc. So it was an upper class sport. Very generally speaking colonisation in India began as a set of military bases to protect the interests of the British East India Company against local rulers as well as other European powers like France (ie. the fighting between France and Britain in The French and Indian War- or the Seven Year's War in Canada, 1750s-60s). Some of the top ranking, most prestigious military positions in the British military could be purchased. So in the military there was a definite distinction between the upper class gentleman officers and the usually poor soldiers. British gentlemen had a whole slew of activities that centred on their identity, and what they did in leisure very much contributed to the identity of a gentleman, because, well only they could afford to do these activities. Cricket was one such activity. So in the various military posts where there were gentlemen they formed cricket clubs that excluded women and lower and middle class men.

Because cricket was seen as a sport that 'civilised' men, ie upper class aristocratic men played it also became a part of the 'civilising mission.' That is a mission to make (mostly) the Indian ruling class 'civilised' or as Thomas Babington Macaulay famously put it in 1835 to make the 'colonised' " Indian in blood and colour, but English in taste, in opinions, in morals, and in intellect." Part of this was establishing British styled universities, and establishing clubs to reflect the values of a British gentleman like cricket. Some Indian rules of course also wanted to emulate this 'Britishness' to distinguish themselves as rulers so they adopted cricket and other things of 'British taste,' like architecture, etc. There's a lot of literature on the history of sport in the British empire and how sport was used to 'civilise' various Indigenous peoples, this is true for what became Canada where lacrosse was used in Residential Schools as a way to make Indigneous peoples 'civilised.' The gruesome irony here is that the sport was appropriated from Indigneous communities like the Haudenosaunee and then 're taught' to their stolen children as a distinctly Canadian national sport.

Fast forward to the mid to late 19th century where cricket begins to be associated with an Indian national identity and is taken up by (gasp) poor people as well. There's a recent general work on these issues that came out in 2015 with Columbia University Press, Nation at Play if you want to read about this process in more detail. And a tonne of articles written about 'cricket and Empire' or 'British identity, cricket, and Empire.'

Colonisation in what became Canada occurred somewhat differently. One major difference was that there was not really an attempt to establish a ruling class from Indigneous peoples (this history of why this was is very long and complicated, and not due to there being no Indigneous rulers or nations because there were strong Indigenous nations, but many other complex factors, some having to due with the antagonist of the United States threatening British rule in Canada, and the British need to (early on) respect Indigneous national anatomy and form alliances against a US incursion). In the most populated 'colonised' places in Canada, ie, what is now Southern Ontario, Québec, and the Maritimes large tracts of land were 'given' to aristocratic families as a way to establish a landed gentry- this had to do with British ideas of terra nullis and how to properly establish government. However, in places like Prince Edward Island, where all (except a few 'reserve' lands) land was given to upper class families, these new landlords were basically absentee- that is they did not want to live in Canada. The settlers eventually filled the role of rulers, early on these settlers were mainly from the British middle class (from families that may have 'failed' in some way in Britain and moved to Canada to further their merchant prospects) established their own clubs, that were distinguished from clubs that contributed to upper class identity formation. And importantly, many middle class Loyalists (British colonists escaping the American Revolution) were given incentives like land to come to Canada.

So why lacrosse, and other activities these mainly middle-class British settlers appropriate from Indigneous communities like snowshoeing clubs in Montréal? This question also has a literature that mainly explains the ways in which lacrosse was used to establish a new identity that was distinct from a British upper class one, and lacrosse was great for this as it was considered to have originated from outside of Britain. There's a new book out this fall by UBC press about this, The Creator's Game, that explains this process in detail and chronicles the history of lacrosse. Hope that helps a bit!

Just being pedantic but your dates are way off.

Canada became a nation in 1867 with the passage of the British North American Act (an act of the UK Parliament). Canada achieved independence in 1982.