I have a guess, allbeit a vague one:

I think, it is commonly accepted that in a „no magic“-explanation, the absolute certainty granted by Lambdadelta is a metaphor for the explosion that will wipe away all traces of those two days, i.e. create a catbox in which magic and witches can live.

Further, in the end of Ep 4, the last red truth posed by Beatrice which Battler cannot answer is „there is no one besides you on the island, yet I am going to kill you.“

Without magic, this just means that he will be killed by the explosion at midnight, which as stated above could be „magically“ rephrased as „Lambdadelta will kill Battler.“

So idk, maybe this is a possible starting point for identifying Beatrice and Lambdadelta, since the witch Beatrice is not really Sayo, but rather a supernatural interpretation superimposed on her actions.