Because I really like syntax like Haskell (the type signature is much clearer especially in generic code compared to Java or Scala etc. for example), I'm curious, what is so uncomfortable about the syntax?
There is a wide variety of syntax among mainstream languages, but basic function calls are pretty much all the same.
Take a look at Reason [1] for an example of how a functional language (OCaml in this case) can be made more familiar.
Some of the algorithms for reducing lambda expressions are symbolic, like, say, alpha reduction. But they are not done in lambda calculus itself, as far as I can see; they are done on lambda calculus (by the mathematician, or a machine for manipulating lambda calculus terms).
Analogy: just like ordinary algebra doesn't have symbols; but of course mathematicians work with symbols and so do computer algebra systems.
Since lambda calculus is Turing complete, it can of course represent lambda calculus manipulation (via Goedel numbering of lambda terms and then working with their arithmetic encoding as Church numerals, or whatever).