I don’t think we’re ever going to agree on this.
A couple of points though:
You say: “an admission of guilt isn’t followed by a reason for the act”. Why not? Why wouldn’t someone say, as an example: “I murdered them because they had an affair with my wife”? I could interpret LL’s statement thus: “I killed then on purpose because I’m not good enough to care for them” as “I killed them on purpose because I’m an unskilled nurse and the babies would have died anyway, so I was putting them out their misery/ending their suffering”.
LL will have no doubt about whether she murdered them or not. She will know what happened. Her language isn’t confused. Her language is contradictory - in that she says both “I haven’t done anything wrong” and “I killed them on purpose because I’m not good enough to care for them”. Both statements are clear in their meaning (to me anyway).
Agree on everything you say except the clarity of the supposed admission of guilt if that sentence was taken in isolation. Yeh that’s my point as well you would only add an explanation in the hope that it ameliorates the wrongness of the act. If it was an admission of guilt you wouldn’t call into question your aptitude as a caregiver ie professional you would say it was because of your mental health and use that as the amelioration. Saying I killed them “because they slept with my wife” is an amelioration of guilt as a wrong has been perceived by the accused not the same as saying “I killed them because I’m not good enough which is saying “I’m just not a good care giver and I know that and my knowledge of these failings means I am culpable in guilt” or “I am not good enough to be a nurse”.
In answer to your question of guilt I am really not sure especially this early. I am looking at it through the lens of trying to bring enough pieces together to build a picture of who Lucy is in terms of her character, the likelihood that she did knowingly administer air embolisms and other acts in hope of it being fatal and her possible motive. Currently have no reason or evidence to assume a motive other than killing for gratification and that at this point isn’t on the cards. Nothing at all to really give Lucy motivation for doing it in the first place. You would have to be a real psychopath to deceive so many people and to kill babies, that would be the worst anyone is capable of and it’s not looking like she has that character seemingly at all. I don’t take the munchausen by proxy theory as there is nothing to suggest attention seeking behaviour or behaviour consistent with someone deliberately causing harm in an effort to elicit attention or adoration. That being ruled out your left with thrill killing, that being at the very end of extremes with nothing to suggest it it’s not likely. IMO.
Edited.
Yes it’s the self contradiction that points at doubt, the polarity of guilt is obvious but when one contradicts oneself it suggests doubt, as in the middle ground between guilt and innocence of murder being it happening by mistake. Considering she would without a doubt be aware if she had committed murder she wouldn’t entertain the idea that these things happened by mistake.
I’m trying to look at it as well from both angles, guilty or not and trying to put myself in her shoes and then figure out what I would be thinking that would make me say the specific things she did in that note. That’s why I would use the other writing to build a picture that provides the context.