Spoiler Warning: this page contains detailed plot
For those of you who rely on visuals I have provided a simplified version of my Timeline Chart as well as small diagram depicting the events of Chrono Cross.
Chart One: Complete Timeline Illustration
Let me begin by saying there are, in fact, only two timelines included in this illustration: the dimension in which Crono lives and an alternate dimension in which Reptite civilization has flourished. As some of the events in Chrono Cross overwrite parts of the Chrono Trigger timeline I have instead drawn two timelines, one showing the events leading up to Lavos' defeat (left) and one showing how the timeline has changed since Lavos' defeat (center). Just remember they are the same dimension. The center timeline simply overwrites the original (left) due to the Time Crash.
The entirety of Crono's adventures took place in the Chrono Trigger timeline displayed on the left. This means that whenever he traveled through time he merely changed his position along the timeline. That is, until he chose to battle Lavos in 1999 AD (The Day of Lavos). After Lavos' defeat, the devastated future ceased to exist and humanity was allowed to prosper. Figure A shows this shift. In this now peaceful future the research installation of Chronopolis was eventually built. In the year 2400 AD a disaster occurred which sent Chronopolis 10,000 years into the past. This event was known as the Time Crash. Figure B illustrates this as Chronopolis (CP) was pulled into the past. Upon arriving in their new era, the Chronopolis workers quickly discovered that another city had been pulled through time as well. This city was known as Dinopolis. For reasons not fully understood, Dinopolis (DP) was brought into the human's timeline from an alternate dimension; a dimension where the Reptites had continued to exist and had even evolved over the millennia. It was in this new era (presumably 7600 BC) that the El Nido Archipelago was constructed by FATE, the supercomputer functioning inside of Chronopolis. From this year forward El Nido continued to exist, forever changing the history Crono once knew. So it is that upon returning from the battle with Lavos (Figure C) that Crono finds himself in a world where El Nido has existed for millennia. Thus, the Chrono Cross timeline has forever changed the timeline present in Chrono Trigger.
Chart Two: Events of Chrono Cross
This diagram is rather straightforward and requires little explanation. It details the events of Chrono Cross from the time shortly before Serge's birth until his adventure in 1020 AD.
It is uncertain what year Lucca was abducted by Lynx if we look strictly to Chrono Cross for the answer . All we really know for certain is that it occurred after the time split. However the date is supposedly given in the Chrono Cross Ultimania Guide: 1015. It also states that the incident took place in both timelines. For the time being this is the only evidence we have showing what fate befell Lucca in Home World, since the game made no comment on this.
If at all possible I chose to overlook information from outside sources such
as the Ultimania Guide. From what I have heard the book is inaccurate in
certain aspects and potentially has glaring inconsistencies with the game.
I cannot verify if this is true as the guide was published only in the Japanese
language, so I am having to rely on segments translated by fans which have
been posted throughout the internet. Even so, I see no reason to doubt the
validity of the orphanage information as it does not seem to contradict anything
shown in Chrono Cross. Just be cautious when using the date of 1015
given the uncertainty of its source.