The first raid instance to feature a “Looking for Raid” difficulty was Dragon Soul.
Looking for Raid, commonly abbreviated LFR, debuted with World of Warcraft patch 4.3, “Hour of Twilight,” in late 2011. The feature gave players an automated way to assemble a large group across servers and enter a specially tuned version of Dragon Soul, the Cataclysm raid centered on the battle against Deathwing.
Dragon Soul’s LFR version was divided into two wings, with four boss encounters in each wing. It used a 25-player format, but the automated queue and reduced difficulty made raid content accessible to players who did not belong to an organized raiding guild. Loot and rewards were also tuned below the normal and heroic versions.
The answer is not Siege of Orgrimmar or Throne of Thunder, both of which came in the later Mists of Pandaria expansion. Icecrown Citadel also predates LFR: Wrath of the Lich King had cross-server Dungeon Finder technology, but not the separate raid-finding difficulty introduced for Dragon Soul.