Since Lavos is the accumulation of genetic data, the spawn of that lavos should contain the genetic data of the previous Lavos.
So since Lavos has the accumulation of DNA of a previous Lavos, isn't it likely that the form you fight after the shell is the accumulation of the DNA of the previous Lavos, while the final form is the developing DNA gathered on earth. It's clear that the final form is the accumulation of all of Earth's DNA, as pointed out by the party, but no mention of this is made by the party fighting the second form.
The final form does resemble the second form somewhat, so it's plausible to think that it is a combined version of the DNA on earth and the previous DNA gathered. So, the shell acts as its vessel and large scale weapon, while the second form acts as a sort of womb for the developing lavos core.
So basically, since Lavos acts as a three part system, it seems like you fight three different entities rather than just three forms of the same being.
So this is my theory. Since the game seems to suggest that the second and final form are separate entities, it is likely that the second form is the pinnacle of DNA harvesting of the previous planet. When that being was created on the previous planet, The womb (the equivalent to the current second form) dies, allowing the departure of the new being.
This Lavos would then seperate itself several times asexually, each one being a shadow of the unseparated form (explaining their absence in the lavos spawn). The new lavos would each grow a lavos shell, develop until a certain point, and then head to a new planet. So Death Peak, instead of being Lavos after creating its offspring, is really just the shell and womb, while the core exited, seperated, and became the Lavos spawn you fight on Death Peak.