Your answer is useless to the commenter you are responding to. If he would 'get' lambda calculus by studying the Curry-Howard isomorphism or the Hindley-Milner type system, he already would have. It is like showing someone that asks about rocket science a calculus book or a rocket and saying: just study how it works. For many people that is completely backwards.

First you need to teach them what the lambda calculus fundamentally is and why it is useful in small bits. Then you can explain to them how powerful it gets, by explaining how the usefulness is extended by the Curry-Howard isomorphism and how you can build the Hindley-Milner type system with it.

The commenter is an 'engineer' and you're a 'theoretician'. As a fellow 'engineer', I completely understand his exasperation with all this pointing to either nice theoretical results or the large scale end products of the theory. That's just fundamentally not how we learn.