The White Lions are Andoran soldiers who have sworn fealty to the Lion Throne of Andor, as opposed to the Queen of Andor.
The White Lions were recruited by Rahvin, posing as a western Andoran lord named Gaebril to replace the Queen's Guards. Rahvin had designs to claim the Lion Throne for himself, and needed the swords to achieve his goals as the Queen's Guards would have fought him to the end.
After Rahvin was destroyed by balefire wielded by Rand, and Rand himself had taken control of the city, the majority of the White Lions fled Andor and ended up near the Spine of the World with Cairhienin rebels.