She is likely named after her grandmother, Lara Lor-Van and was instrumental in the final overthrow of Brainiac, and the rescue of the bottle city of Kandor.
Lara grew up on Paradise Island, never knowing much of her father or the outside world. Her parents wanted to keep her hidden from Luthor and Brainiac's ever-watchful gaze. However, she was forced to reveal herself when her father is about to be killed by Brainiac; interveining in the battle and saving his life. With the government demanding that she be handed over, Lara goes into hiding with Batman alongside her mother and father. She bombards Superman with a barrage of questions, and also demonstrates her poor opinion of people less powerful than herself. She even tries to persuade her father to rise above the "humans" and maybe even take over the world.
The group devises a plan to bring down Luthor and Brainiac once and for all; by having Lara pretend to hand herself over to Brainiac, the Atom is able to slip into the bottle holding the city of Kandor and free the Kandorians who use their combined heat vision to destroy Brainiac, subsequently destroying the power source of the government's dictatorship and inciting a revolution.