Lambdadelta being the piece of candy that is used many times in the story as proof of magic and what initially convinced Maria that Beatrice exists, the way Lambda endorsing Sayo as a witch works as an allegory for how the candy trick made Beatrice 'exist' through Maria's belief/acknowledgment and how that was the foundation of Mariage Sorciere and the concept of endless magic VS Bernkastel being the black cat that Kumasawa blames to get Sayo out of trouble when she breaks Kinzo's vase, something that's depicted as Virgilia's finite magic, Sayo's first exposure to magic as a way to actively avoid the harshness of reality which translates to young Beatrice's decision to become Virgilia's apprentice, the way Bern's position in the story seeking to dismantle the illusion of the witch as cruelly as possible reflects how this kind of magic is only temporary relief and reality always supersedes it, you can blame a cat for the vase being broken but it's broken nonetheless and it's easy to prove that the cat story was a cover up, the consequence to lies being piled up on top of lies is that when the truth eventually comes out, it becomes much more devastating (see: Sayo being lied to about herself her whole life)
Lambda and Bern existing as meta-phors not just for two concepts of fate but also two different conceptions/origins of magic, the candy and the cat being keys in pivotal moments where magic first "came to be", the candy magic revolving around truth being created by belief and the cat magic being about escaping truth by creating a lie