In the short run, the American Revolution was not inevitable, but in the long run, the colonies could never have remained part of the British Empire.
In the short run, the American colonies' demands could surely have been accomodated by a more flexible British response. Giving the Americans representation in Parliament in 1763 would have surely gone a long way to reducing the tensions between colonies and mother country. This sort of flexibility would likely have kept the Revolution from happening.
In the long term, though, the relationship between the two had to change. The colonies were becoming too big and too important to remain subordinate forever. At the very least, the colonies would have had to have been given autonomy much like Canada was in the mid-1800s.
So, in the long run, the colonies could not have remained as colonies. They would have become to some extent independent in the long run even if war could have been avoided in the 1770s.
We should also point out that the fall of the British Empire and the loss of the American colonies following the Revolution were not necessarily inter-related nor in the same time frame.
At the time of Lexington and Concord, barely more than 1/4 of the colonists seriously supported independence, while at least an equal number were actively loyal to the Crown. Clearly, this was not a black and white sentiment on either side, and had things been handled differently by the King, perhaps independence would have come much later.
I actually believe King George III showed quite a bit of patience until 1773. He was wiser and more pragmatic than many historians give him credit for, in my opinion. His subsequent overreaction, however, to the Boston Tea Party (with the Coercive Acts) and his refusal to negotiate with the cooler colonial heads following Lexington and Concord (when they offered the Olive Branch Petition) would mean Britain's eventual imperial undoing in North America. That is, the King and Parliament ignored the voices of reason among them, such as Edmund Burke, and in reacting aggressively and sending an army and navy, further pushed the colonists in support of a revolution.
While I still feel independence would have been inevitable in the long run, under what terms would it have come? Like those of Canada, far in the future and much more peacefully? Would it have come in fragments, with sections of colonies breaking away while others stayed with the Crown? Would the French Revolution have occurred when it did, had the American Revolution not taken place at that time? Thought provoking questions.