"That goat is like a little gold mine".~Katniss Everdeen, 74th Hunger Games
When Katniss first saw Lady, she belonged to the Goat Man. Katniss had shot a deer and gotten a decent price for it. She wanted to buy Prim something for her birthday, so she went to the market on the square to buy dress fabrics, when the Goat Man and his herd of goats caught her attention. Lady was lying down in a cart, because her shoulder had been bitten and infected, probably by a dog. Katniss wanted to buy the goat for Prim, realising it would make her even happier when she could also take care of the goat's wound. The goat was originally going to be bought by Rooba, a butcher from District 12, for slaughtering but Rooba recognized Katniss trying to buy the goat and let her have Lady, saying: "Look at that shoulder. Bet you half of the carcass will be too rotten for even sausage. Sell her to the girl if she's stupid enough to take her." with a wink to Katniss. Katniss bartered with the Goat Man for half an hour but ended up getting to a price. Immediately after purchasing Lady, Katniss bought a pink ribbon and tied it around the goat's neck.
Prim was so excited when she got the goat that she cried and laughed all at once. Even though Mrs. Everdeen was worried about the goat's odds of survival, Prim and Mrs. Everdeen managed to restore Lady to full health.
Lady didn't make any appearances in The Hunger Games film. However, Katniss mentioned it to Prim that she can make cheese from her goat's milk when Prim and Katniss' mother visited her before Katniss was to leave for the Capitol.
In Catching Fire, it was mentioned by Katniss that she and Prim wanted Lady pregnant.
In Mockingjay, Lady is assumed to have died in the firebombing of District 12. Katniss goes back to her old home in District 12 after the bombing, but can only find Buttercup, Prim's cat, and not Lady, so Katniss assumes that Lady died. Even if she survived the bombing, she had most likely died of starvation or wounds sustained during the firebombing.