There are several different women who take up the name Lady Liberty:
I: She was a member of Force of July and died fighting against Kobra.
II: The mantle of Lady Liberty was taken up much later by a hefty African-American woman, who had been granted superpowers through Lex Luthor's Everyman Project. Her fate following the "Rain of Supermen" event, which depowered and killed off most of the recipents of the superhuman abilities granted by the Project is unknown.
III: As a member of Freedom's Ring she was task to protect the remains of Bludhaven after the Brotherhood of Evil devastated the city using Chemo as a living bomb. The Ring's mission was to secure the area, so that S.H.A.D.E. could begin studying and experimenting on those who had gained metahuman abilities in the wake of the massive burst of radiation emitted in the aftermath of the explosion She was killed by Geiger of the Nuclear Legion.
IV: After S.H.A.D.E. takes over Freedom's Ring, a new operative is given the costume and codename. Like the second Lady Liberty, she too is African-American, and sports a stylish dreadlock variant of the typical hairstyle worn by those operating under the codename. However, she is killed by Ravager during a conflict with the Teen Titans, Firebrand IV, Monolith, and the various superhuans inhabiting Bludhaven.
V: A new Lady Liberty fights the Freedom Fighters as an agent of S.H.A.D.E.'s newest superhuman assault team, First Strike. She appears to have some previous relationship with the new Phantom Lady, stating intense distain for her during their fight. She manages to enrage Stormy enough to the point that she lashes out at her in anger and strips her of her costume with her Blacklight Ray, and therefore, the source of her powers, during their fight midair. If not for a timely rescue by The Ray, she would have been killed as a result of her fall back to Earth. Instead, the Ray took pity on her, stating that hey weren't the bad guys here, and used his superspeed to wisk her away to safety, thankfully somewhere her current, attireless appearance wouldn't be out of place: a nudist beach in Spain.