After being bullied by a couple of fellow mutant children, Lita runs off, crying. Jennika gives her a pep talk, recounting the words of Splinter, who told her that she is ninja, and that this applies to Lita, too, and that he said "you are the future, and the future is limitless".
Just then, a grown-up Lita appears outside the farmhouse with the Time Scepter. TMNT #105
Lita finally finds the Splinter Clan at the dōjō, bringing dire words of a future where the Splinter and Foot Clans clash, resulting in Jennika killing Karai and the rapid dissolution of Lita's family. She leads the Splinter Clan to where Karai's helicopter had crashed, and they rescue her, Koya, and Bludgeon from the wreckage and bring them back to the dōjō. TMNT #113
Lita was a member of the Splinter Clan until it fell apart following Karai's death. She sees the Clan as her family and addresses Donatello and Leonardo specifically as "dad".
Owing to Leonardo and Koya apparently being an item before his disappearance in her timeline, Lita addresses Koya as "Auntie", much to the falcon's bewilderment and disgust.
Lita was left alone with nobody else to turn to, and was taken in by Renet. Under her tutelage, Lita is an assistant timestress.