It's easy to miss since it's a small link near the top of the post, but something that will help a lot in understanding this post is this video:

The most beautiful program: https://www.youtube.com/watch?v=OyfBQmvr2Hc

It essentially gives you a quick 5-min overview of the lisp language, then shows you how to implement lisp in lisp with only a few lines of code.

IMO, understanding lambda calculus is much easier for the uninitiated after watching that video.