From Dragon Ball Encyclopedia, the ''Dragon Ball'' wiki
Lime (ライム, Raimu; FUNimation "Lime") is the granddaughter of Lao Chu.
Lime's Japanese name is a pun on the word Raimu, or Lime in English.
Dragon Ball Z
Lime appeared in "A Girl Named Lime". She met Son Gohan before the Cell Games. Her parents had been victims of Imperfect Cell, therefore she lived with her grandfather, Lao Chu, who owned a shop in Chazke Village. She met Gohan after she fell off a tree and into a river while trying to reach an apple. Gohan saved her and later helped her destroy Bourbon's Protective Dome.
It is assumed that her parents were brought back to life with all of the other victims of Cell by the wish made after he was defeated.