I'm not sure that it's entirely accurate to describe C S Lewis as a Protestant. Anglican, yes. But it seems to me that his theology - probably accepting purgatory, for example - was very much on the Anglo-Catholic wing.
An Angelican is a Protestant. It was formed by King Henry VIII in 1533 during the Protestant Reformation with inspirations from John Calvin and Martin Luther. That, Lutheranism, and Calvinism are the three main denominations that all of the other Protestant denominations base their beliefs on.
And you are right that it is mainly an Anglo-Catholic thing. The main thing that King Henry changed was he got rid of the pope so he could annul his marriage. Other than that, it is essentially the same as Catholicism; none of the core beliefs were changed. But because it happened during the Protestant Reformation and was inspired by Martin Luther, it is by definition a Protestant denomination, which means that C.S. Lewis was a Protestant.