I think that what ever direction your lanai faces you will compensate for the weather. Too hot?? pull the blinds and use it in the AM. To cool? get one of those outdoor fireplaces or heaters. I think a lanai is beautiful, which ever way it faces. That's one of the reasons I like Florida. You guys have lanais and we have decks. The lanais get much more use than a deck.
The perfect direction is the direction YOURS faces!!!
enjoy