I think the issue here might be the overloading of terms - lambda calculus is both the system of notation and the common name for the conceptual underpinnings of computational theory. While there is little to no similarity between the abstracted study of change over a domain and a notational system, the idea of function composition or continuous function theory (or even just computation as a concept) are all closely related with basic concepts from “calculus calculus” like limit theory and integral progression.

edit: clarity