Ok, I've looked and I haven't noticed any topic like this, so please don't kill me if I'm copying something.
Now I'm currently playing Chrono Cross for the first time, and whilst I've been told over and over again by different people that Lucca and Luccia can't possibly be the same person, I've still constructed a comparison, as well as a theory onto how they could possibly be the same person.
Pros for Luccia being Lucca:
Name - a very weak point, but Square hardly ever do such similar names without reason (for example, Rikku from Final Fantasy X was originally meant to play Yuffie's part in Kingdom Hearts, this was changed due to another character, Riku being in the game)
Appearance - a lot of people I've talked to have tried to tell me that they don't look alike, however, basic appearance, they both have purple hair, contained somehow (it would seem that headgear is appreciated with the girls), and both wear glasses. The difference in artwork could be simply put down to the fact that the two games had different artists, plus she could have changed a lot in the time thats passed.
General abilities - well first their similarities, they're both brilliant scientists, and just generally clever. In battle they differ, in both weapons and magic, however, we must remember that the magic style of El Nido is different to the magic wielded back on the Zenan Mainland. The weapon is easy enough, she is intelligent, so I'm sure she'd be able to learn how to master a different weapon.
Viper Manor - ok, here's a weird one, assuming what I say under "age" in cons (just check down), is correct, why would she take a post in Viper Manor? Simple pimple, in order to be near Lynx, she could be expecting Kid to come looking for Lynx, in which case she'd be there for her, she could also be wanting to make sure that the future she helped to create would go on to exist, and not be destroyed.
Cons for Luccia not being Lucca:
Luccia knowing Lucca - Luccia admits to knowing Lucca, and that Lucca gave Luccia a letter to give to Kid, however, a point against this is that Lucca could easily be lying, she could just pretend not to be herself in order to protect Kid, since all of Kid's life post-Lucca "dying" was all about avenging Lucca's death. Another way to look at this is that maybe Lucca lost her memory from being close to the Frozen Flame, FATE managed to manipulate Serge's father, why not manipulate Lucca's memories, make her believe she was someone else?
Age - now this is the one that cause me a lot of hassle, Luccia is *supposedly* 28 years old, this would make Lucca only 8 in Chrono Trigger, which of course she isn't. And yet, I'm about to turn this con into a pro... My answer came to me when I discovered that Lucca was doing different types of research after Chrono Trigger, including circuit research (aka, the Prometheus Circuit) as well as more research into Time Travel, she was also the developer for the Mother Brain program, this sounds like way too much to be done in only 5 years (I'm trying to remember when it was that Lucca's house was set on fire). Now Lynx and Harle took Lucca to Chronopolis if I'm not mistaken, in order to bypass the Prometheus Circuit, however, she refused, or whatever, and they end up leaving her for dead, Lucca however, could have used a method of travelling a certain amount into the future, maybe he method wasn't complete, or maybe she only wanted to travel to safety, and hence why she's not as old as she could be.
Hmmm, actually I've just sort of done my entire idea, in this section that was meant to act as an intro, oh well, please feel free to continue talking about this, I'm really hoping to see how other people look into these things.