According to the official schedule, the fourth and final wing of the Siege of Orgrimmar, "Downfall," should be available as of today, October 22nd, to players via LFR. The fourth wing features three bosses: Siegecrafter Blackfuse, Paragons of the Klaxxi, and the big bad Garrosh Hellscream himself. As has always been the case, you much have the achievement of completion for the previous raid wings in order to access the new one, in addition to a minimum gear ilevel of 496.
With this last stage of the raid unlocked, LFR groups should now be able to complete the entire Siege of Orgrimmar. If you've somehow managed to avoid all the spoilers as to the identity of the new Warchief, now's your chance to find out the old-fashioned way!