The case against prayer (I mean the 'low' or old-fashioned kind) is this. The thing you ask for is either good—for you and for the world in general—or else it is not. If it is, then a good and wise God will do it anyway. If it is not, then He won't. In neither case can your prayer make any difference. But if this argument is sound, surely it is an argument not only against praying, but against doing anything whatever?
In every action, just as in every prayer, you are trying to bring about a certain result; and this result must be good or bad. Why, then, do we not argue as the opponents of prayer argue, and say that if the intended result is good God will bring it to pass without your interference, and that if it is bad He will prevent it happening whatever you do? Why wash your hands? If God intends them to be clean, they'll come clean without your washing them. If He doesn't, they'll remain dirty (as Lady Macbeth found) however much soap you use. Why ask for the salt? Why put on your boots? Why do anything?
C.S. Lewis, “Work and Prayer,” God in the Dock (Eerdmans: 1970) 105.