We had our lanai tiled and had a similiar problem with rain water pooling in spots. My husband drilled small holes though the grout to the outside wall. He lined the hole with a small (think straw size) tube and then affixed little pieces of screening on the outside wall. No more pooling. We had called about the drainage things but the man wanted to remove several tiles and that was not acceptable to us. This seems to work very well for us.
