The main issues, well l-calculus is extremely important because this notion of b-reduction formalises the notion of capture avoiding substitution of bound variables.
l-calculus was first used by Church, Turing and Rosser to formalise the notion of computer algorithm and in fact Church's thesis originated precisely when Rosser and Church together with Turing realised that all Turing computable functions are l definable; and they succeeded to prove also the converse, that is all l definable functions are Turing computable.
A very interesting point is if this language is the basic, the fundamental paradigm functional language: how do we represent the recursive functions, and how do we represent data types?