I guess with the many different replies we have not given you a definative answer. Our lanai faces east. This was by accident not design, however it turns out to be the way we prefer (especially since it would be hard to change

). I personally would not want afternoon/evening sun. It is VERY hot here in the summer. My parents home has a west facing lanai and they had to put up blinds inside the lanai that they raise in the afternoon. This cuts down the heat but also eliminates the only advantage to the west facing which is pretty sunsets.
jeffy