[ericssmith]

I'm not sure what you mean by "equivalent", but historically, the "computer science problem" that lambda calculus has been used to address is understanding the meaning of expressions in programming languages. The first paper to introduce lambda calculus in relation to computers was Peter Landin's "The mechanical evaluation of expressions" (1964). Its specific goal was to use the lambda calculus to model the facilities of other programming languages in use at the time. Landin continued this investigation with two more papers in the series: "A Correspondence Between ALGOL 60 and Church's Lambda-Notation" (1965) and "The Next 700 Programming Languages" (1966). Because of the LC's basis in mathematics and logic, it provided a useful way to define the semantics of programming languages. It continued in this role over the next few decades. One of many high points in this evolution was the use of the LC as the basis of Scheme, "An Interpreter for Extended Lambda Calculus". Among many other contributions, the "Lambda Papers" investigated other models of computation (e.g., actors).

So the lambda calculus has been used as a consistent and primitive basis for understanding computation itself and how it is expressed in programming languages. I suppose it is more "equivalent" to Newton's 2nd Law than any particular way to solve a problem. It's perhaps worth remembering that Principia used geometry, not what we know of as calculus, to clarify mechanics.