So, it doesn’t look as if Beate’s imaginary (?) friend is actually based on Lottie. Beate’s reaction to Lottie and Claire in that final panel indicates she knows who they are, but it’s not the reaction I’d expect if she saw herself specifically as Lottie’s protege in some way. Also, the Imaginary Friend’s hair resembled modern Lottie’s more than Lottie at the time’s. And we never saw her face.