Were any lessons learned & applied?
The Canadian Rebellion of 1837-38 aroused fears in Britain that this was a second American Revolution. Lord Durham's classic state paper of 1839 recommended that self-government within the Empire was the only policy that would retain Canada within the Empire for the long-term.
Consequently, the concept of Dominion status was invented whereby the British settler colonies in Canada, Australia, New Zealand and South Africa were domestically and economically completely independent, whilst Britain used the Royal Navy's supremacy to protect them.
One of the important American grievances against Britain had been its restrictionist mercantilist economic policies. The reaction against this led to the opposite extreme: the somewhat ludicrous situation arose where Dominion's put up tariffs against British imports into their ports but in the same ports the British warships that were protecting them were anchored.
The Durham tradition led to the Liberal government granting South Africa Dominion status a few years after Britain's victory in the Boer War. However there was also reaction against self-government in the late 19th and early 20th centuries in Britain. For people like the Liberal Unionist Joe Chamberlain, it seemed like the Dominions were growing apart from Britain and would eventually break away completely. His solution was imperial federation, although New Zealand alone out of the Dominions was wholeheartedly in favour of this. The differing strategic interests of the disparate Dominions made any federation hard to achieve, along with strong Liberal opposition to this within Britain.
In short, the loss of the American colonies led to a reappraisal of the idea of empire away from the view that colonies existed to enrich the mother country to liberal ideals of self-governing communities held together by sentiment.