CC is a sequal of CT. Forgive me if my little spoiler hear is off, Haven't played cross for a while.

(SPOILER)Before Lavos was defeated, he pretty much made a backup of himself. That was the Frozen flame. In one Timeline, Fate was created to manage the future and all futures of this planet. However Fate couldn't control one Aspect, the Frozen Flame. Chronopolis, the place where fate Was created, sealed away the Frozen Flame. In Chrono Cross, the main character came in contact with the frozen flame and was chosen by it. Serge, the main character, was no longer under control of fate. Lynx was sent by the Frozen Flame to Serge, who being the last Person Chronopolis registered as entering during the time its power went down, the same time serge came in contact with the flame. Serge was now the only one who could access the Frozen Flame.

Thats what I can remember now, please correct any mistake I may have made.