I'll reiterate what Liam said - there was a chemical trace of injected (rather than natural) insulin found during post-mortem. That's the smoking gun. At that point, the question necessarily moves from why did these babies die, to 'how' did these babies die - and the answer, statistically speaking was Lucy Letby. A post-it note may not have helped her case, but it certainly wasn't what put her behind bars.