What was the original intent for the creation of Lambda calculus?
He wanted to create a formal system for the foundations of logic and mathematics that was simpler than Russell's type theory and Zermelo's set theory.

The basic idea was to add a constant $\Xi$ to the untyped lambda calculus (or combinatory logic) and interpret $XZ$ as expressing "$Z$ satisfies the predicate $X$" and $\Xi XY$ as expressing "$X\subseteq Y$". With rules expressing these intentions one can then interpret the ${\to}{\forall}$-fragment of intuitionistic predicate logic and unrestricted comprehension, the only problem being that by Curry's paradox, every $X$ is derivable.

See p. 7 of:

Cardone and Hindley, History of Lambda-calculus and Combinatory Logic, 2006:
http://www.users.waitrose.com/~hindley/SomePapers_PDFs/2006CarHin,HistlamRp.pdf

As well as the introduction to:

Barendregt, Bunder and Dekkers, Systems of Illative Combinatory Logic Complete for First-Order Propositional and Predicate Calculus, JSL 58-3 (1993):
http://ftp.cs.ru.nl/CompMath.Found/ICL1.ps