I just looked at the notes written by LL again and although the defence are stating "I killed them on purpose" amounts to anguish and not admission, I really can't see how this could be interpreted as anything other than an unambiguous confession to murder.
It's not "I accidently killed them" or "I made mistakes and they died" or "they're saying I killed them on purpose" or any of the millions of other permutations that could be used in order to desparatly protest your innocence.
She is having a moment of clarity and she's anguished because she's recognising what she has done and stating it in very clear terms to herself. The point to prove for murder is killing another with intent, she offers it up with the words "on purpose". They are plain, clear and unequivocal words which no amount of linguistic gymnastics can explain.
Whatever spin the defence try to put on it, there is no way an innocent person, however anguished would write those words if they hasn't killed those babies "on purpose".