I was finally able to get TypeQL working with Netlify Functions / AWS Lambda after a day of work, going over the docs and examples, and in the end desperate brute force.
I'm sharing my working code here for others (or for future reference of my own :P ) as it contains some counterintuitive keyword usage.
Normal Approach
The error I kept getting when using the simple example was:
Your function response must have a numerical statusCode. You gave: $ undefined
I searched of course in the issues, but none of the suggested solutions worked for me.