Metatextually, Dr. Light is there because someone in editorial told McDuffie to put her on the team.
In-story, Dr. Light is there because Starbreaker disabled the Shadow Cabinet's teleport system, and Dharma hatched a roundabout plan to fix it. In exchange for getting her powers fully restored, (they've been off and on, thus "explaining" her contradictory appearances in different books), Dr. Light fixed the Shadow Cabinet's teleporter. At the end of that, Dr. Light wound up in JLA HQ, and since they were having a bit of a personnel shortage, the Justice League invited her to stay.