I don’t think it’s been PROVEN yet that Lagi is reborn in every game. There are still enough elements that point to Lagi being the exact same dragon in the whole series.
Especially in Orta, the way the story and backstory is explained, and especially the recorded “dialogue” between Lagi and the heresy program (we can only really hear the heresy program during that sequence), imo it’s pretty self eplanatory that Lagi is in no way reborn after the end of Saga, but simply exits Sestren space, this time leaving the heresy program behind leading to him returning to his more animalistic coolia origins, thus the large difference in appearance.
This could also be the reason he can now sort of reproduce, as it is told at one point in Saga that dragons can’t reproduce and yet we have no idea on how the coolia go about doing that (unless it’s explained somewhere in the Orta Pandora’s Box, I wouldn’t know).
On the other hand, seeing as the heresy program was a pretty advanced life form in its own right that caused Lagi to evolve several times throughout the games and aquire special skills, it may also be the reason behind this new found ability as well.
Anyway, I like to think it’s the exact same coolia originated dragon in the whole series. Why? Because if we assume the opposite then we pretty much accept that the original creature the heresy program possessed was nothing more than a pet, a mindless drone, an expendable creature only used for the heresy program to achieve its goals. Not something that Lundi formed any kind of bond with during his journey, not something that has feelings and cares about what’s happening just as much as the rider and the heresy program itself.
And if that was the case, then why would the heresy dragon care about any of its future hosts then, if it switched between expendable hosts on every chance? Why would it give the “new” creature in the end of Saga the chance to decide if it wanted to go back to the world? What made this particular host more important than the host the heresy program used during Zwei?
I hope everybody understood the way I’m thinking about this. In short, IMO it’s the same dragon in the whole series, not just the heresy program part, but also its other half, its first host, the mutated coolia Lundi raised. 