But if you are looking for First (or perhaps even Business) class, many (most?) airlines really open up availability in the 2 weeks prior to the flight. I know that Lufthansa does this for First.
Also, Cathay does it - I've personally redeemed American miles for Cathay First within a week of travel. United does it as well.
Swiss (which is owned by Lufthansa) does this as well - for shorter flights (intra-Europe), they usually release award seats 2 months prior to the flight - we recently redeemed United miles for Athens - Zurich.