Two thing just popped in to my head,
1. Is it so hard to believe that they were misusing the word Daughter-clone?
2. Lavos could vary well be parthenogenesis, as there are offspring in the year 2300A.D., then while Schala was joined with Lavos she could have used Lavos' biology to provide means to produce Kid, there has been a dog that give birth to kittens, and hornets reproduce in tree's for nutrition.
1 - This is actually a very good point, and the answer depends on how the Japanese script reads. If it says 'daughter' without the 'clone', then yes, the English translation of 'daughter-clone' is almost certainly incorrect and something else is at play. If it says 'daughter-clone', then no, unless somebody screwed up in the writing department and they simply used the wrong word (which, I have a hard time believing, because most people today know what a clone is). If someone is a clone, they are a genetic copy of the original subject. Parthenogenesis creates a new, recombined, individual genome--a
daughter, not a daughter-clone.
2 - Well, yes and no. The possibility that Lavos uses parthenogenesis to reproduce is high, yes. It seems that he uses some form of asexual reproduction at the very least. However, since it is through an ovum (egg) that parthenogenesis would take place, and the human ovum cannot divide under any significant length through a similar process, then the egg that Schala would have to use would be Lavos' ovum, in which case Schala's DNA would never even enter the equation. The very definition of parthenogenesis is that it uses
one egg, and recombines the DNA accordingly, and uses
no outside DNA. If somehow she had managed to insert her own genetic material inside of Lavos' ovum, the genome would have to be modified in order to allow for the fertilization to happen in the first place. Kid would be the genetic daughter of both Lavos and Schala (and as Zeality pointed out earlier in the thread, she would take on some of his characteristics, like spikes and such). She wouldn't have 'just a little' of his DNA, she'd have half his DNA, cause he'd be her father.
Short of some incredible, god-like spell, Schala could not reproduce asexually using her own eggs. In order to do so, she'd have to carry the child herself, and then continuously hold this spell for several weeks into the growth of the fetus to guide its development--maybe even longer. And again, if she uses Lavos' eggs, it becomes something else entirely, because then Kid would have two genetic parents--Schala and Lavos. That would be fertilization, not parthenogenesis. I seriously doubt she had that kind of energy and time to drive into a spell.
Another option is that she inserted her own genetic material inside of an ovum, fertilizing the cell and thus cloning herself. The cells would divide normally, and as I've said earlier in the thread, a tiny amount of genetic variation would occur as the fetus grows. The epigenome would develop to be completely unique. This is
not the same as asexual reproduction.
By the way, the 'dog giving birth to a kitten' story is actually not true. The dog in question gave birth to a dog with a gene mutation. It looks like a cat, but is a dog.
http://www.ananova.com/news/story/sm_2371905.html