Core Aldwych is a simple model for concurrent computation, involving the concept of agents that communicate through shared variables. Each variable will have exactly one agent that can write to it, and its value can never be changed once written, but a value can contain further variables that are written to later. A key aspect is that the reader of a value may become the writer of variables in it. In this paper we show how this model can be used to encode lambda calculus. Individual function applications can be explicitly encoded as lazy or not, as required. We then show how this encoding can be extended to cover functions that manipulate mutable variables, but with the underlying Core Aldwych implementation still using only immutable variables. The ordering of function applications then becomes an issue, with Core Aldwych able to model either the enforcement of an ordering or the retention of indeterminate ordering, which allows parallel execution.