"What sort of evidence would prove the efficacy of prayer? The thing we pray for may happen, but how can you ever know it was not going to happen anyway? Even if the thing were indisputably miraculous it would not folow that the miracle had occurred because of your prayers. The answer surely is that compulsive empirical proof such as we have in the sciences can never be attained."
We cannot prove the causality of prayers to God and what we see happen anymore than we can prove the cause and effect of our "prayers" to man, Lewis says. For example, just yesterday my wife and I thought it would be nice to end our Sunday evening with a trip to the ice cream shop. We considered inviting our neighbors, as we were sensing we needed the company of friends, but thought they had a long weekend and we ended up traveling alone. We arrived, got our ice cream and sat down, and then looking over, we saw our neighbors drive up! They came anyway and we enjoyed ice cream together, even though we failed to ask.
So, why pray if we can't really prove the causality of our prayers? Does prayer really work? This question "puts in the wrong frame of mind from the outset. 'Work': as if it were magic, or a machine - something that functions automatically. Prayer is either a sheer illusion or a personal contact between embryonic, incomplete persons and the utterly concrete Person. Prayer in the sense of petition, asking for things, is a small part of it; confession and penitence are its threshold, adoration its sanctuary, the presence and vision and enjoyment of God its bread and wine. In it God shows Himself to us. That He answers prayers is a corollary - not necessarily the most important one - from that revelation. What He does is learned from what He is."