There was much speculation to this effect during his lifetime and was the subject of at least one letter to Lewis to which he replied rather strongly in the negative.
I took a seminary level course in the life of C. S. Lewis. He’s so popular, everyone from Baptists to Eastern Orthodox or Roman Catholic tries to claim him. So much for “mere Christianity!”
Lewis’ brother, “Warney” a bachelor who lived with C.S. (”Jack” as C.S. Lewis was known to his friends) was a horrendous binge alcoholic. He would literally disappear for weeks at a time, on a bender, and not remember what happened. Very very bad. He was even drunk when Jack died, and that state may have contributed to his ignoring C.S. Lewis’s rapid decline....(and he blamed himself for it...dying not too long afterward, staying drunk most of the time). Anyway, one time after a bender on a vacation Warney was picked up out of the gutter (literally) by some kind nuns at a local Roman Catholic hospital. They nursed him back to health and were so loving and kind, Warney was ready to convert. Jack though warned him in a letter in the most stern terms not to do it, and Warney didn’t.
We must remember, C. S. Lewis was actually Northern Irish in his upbringing, and Welsh in his ancestry—his grandfather a preacher...no background that makes one sympathetic to Roman Catholicism. He was a high Anglican, even fairly Anglo-Catholic (I’m sure they will claim him... believing in a form of purgatory for example—but not as dogma), but that didn’t make him, if you’ll excuse the expression (which Lewis used), a papist.
His views on the Sacraments, Purgatory, and other issues are decided Catholic. Given the direction the C of E has taken since his death, I think it's a toss-up as to which direction he would have gone (and he certainly wouldn't have been very happy with some of the goings-on in the Catholic Church either!)
It's entirely speculation of course, sort of along the lines of trying to decide what Henry VIII really died of.