Destiny and fate do not exist in the Chrono series; that is, no events are predetermined, and anything can be changed through time traveling. In the scope of the timeline, time flows normally until rewritten by time travelers. To make a somewhat mathematical example -- in timeline X, if event Y shall rewrite certain events to form new timeline X', even if event Y surely shall occur, time must flow until reaching Z, the time of Y's occurrence, until X can be rewritten to X'. This may seem overly simple, but it is important to establish free will in the Chrono series, as the ability to alter the events of history to make a better world from the central theme of the games.
Lavos is not defeated until Crono consciously decides to exercise his free will and thwart him, and the Time Devourer is not defeated until Serge makes the final journey to the Darkness Beyond Time. To invoke predetermination or destiny would fundamentally undermine this right. The question of whether events by time travelers have already occurred or have yet to occur is answered by the stablization of the observer's viewpoint. To Crono in 2300 A.D., Lavos still exists, but to Serge, Lavos was defeated. This is merely because Serge was born after Lavos was defeated. Please consult Time Error for more on this subject, and how time traveling events transcendetally line up as a whole.
We can make an analogy here:
Timeline X = 1000 A.D. X' = 1000 A.D. w/Black Omen Event Y = Ocean Palace disaster, raising of Black Omen Z = Time of Ocean Palace disaster (12000 B.C.)
So, to rephrase:
Due to the Ocean Palace disaster, the 1000 A.D. timeline is rewritten to include the hovering Black Omen. The rising of the Omen is unpreventable in the "correct" version of the plot (the one that nets New Game+ and the normal ending), but until the Ocean Palace disaster actually occurs in 12000 B.C., the Omen does not appear in the other time periods.
We can make another example out of Ending #1:
Timeline X = Ruined 2300 A.D. X' = Bright and Happy 2300 A.D. Event Y = Defeat of Lavos Z = Time of Lavos' fall - 1999 A.D. (You could argue 12,000 B.C., or say that Lavos exists in some kind of pocket dimension, or that it's a temporal anamoly... but as long as it's before 2300 A.D. we're good.)
Crono and co. defeat Lavos in 1999 A.D., averting the apocalypse and making the future bright and happy. While its defeat is predestined in CT's course of events, until Lavos has actually been vanquished, the ruined 2300 A.D. future still exists. Free will is a fact.
But what happens if the time travelers go back and murder their ancestors? Does the fact that Lavos's defeat would cause the travelers not to see a Day of Lavos video in 2300 A.D. and as a result not go on their quest? These questions are answered by Time Traveler's Immunity.