sanjibdutta
I am sure you are correct, but I am mystified as to why you should wish to rewrite Map, Reduce, Scan, ByCol, ByRow using Lambda recursive functionality. I believe the helper functions to be more computationally efficient and easier to use than recursion. The present implementations of Map, Scan, ByCol/Row do have a major shortcoming in that they do not return nested arrays (that is, most solutions of interest) but the workaround is to use REDUCE with V/HSTACK being used to build the 2D nested arrays.
As you point out, the LET function, with its local variables, is a key element of writing code with any significant breadth of functionality. For example, I have written formulas implementing Fast Fourier Transform algorithms, both using recursion and Lambda helper functions. The latter version is both more efficient and easier to follow, though the mathematics behind each is not for the fainthearted.