Lambda calculus and it relation to LISP

[gnuist]

I read the following quote in a book on emacs and similar
things in a book on lisp.

"The lambda calculus is a mathematical formalism 
having to do with the way functions instantiate
their arguments. To some extent it is the theoretical
basis for Lisp and plenty of other computer languages."

I am interested in a little concrete elaboration
of this statement by any mathematicians, logicians
or practitioners/users of lisp and lisp in emacs.

This is an interdisciplinary topic and cross-posted.
Please beware of this and be undaunted in intellectual 
work just in case some rude individual jumps in and threatens
the discussion on this thread. This comment is in view
of a sad incident by a similar character on a valid 
interdisciplinary thread on comp.lang.lisp and gnu.emacs.help.
Previously this individual had also posted unbecoming
comments to Professor Fateman of UC Berkeley who is
actually a very nice and helpful individual in my experience
about two years ago from a phone conversation with me.

I think that it would be exciting and intellectually 
satisfying to know an answer to this question for many
of us in the math/logic/lisp/emacs community.