Been continuing trying to figure this out, reworking with netlify-lambda etc. but still no luck in getting it to work when deployed. Latest deploy preview: https://5f5bbebd467d4a00079417aa--cello-lessons.netlify.app/
I really have no idea if it’s firing or not when deployed. I can only assume it isn’t because the form submissions are not deleted. It has never appeared in the Functions UI and the Netlify Support twitter account told me this is normal for lambda functions that are Netlify event hooks like mine (https://twitter.com/NetlifySupport/status/1303766897536581632) Really hard to debug this 
The env vars are correctly set. I have one set custom and the other, SITE_ID, is a default
Deploy log slice so I know that it is being picked up during the build.
8:16:32 PM: │ 2. onPostBuild command from @netlify/plugin-functions-core │
8:16:32 PM:
8:16:32 PM:
8:16:32 PM: Packaging Functions from lambda directory:
8:16:32 PM: - submission-created.js
8:16:45 PM:
8:16:45 PM: (@netlify/plugin-functions-core onPostBuild completed in 13s)
Update
Created a duplicate of the function with a non-event based name. Deployed it. Visited it in the browser e.g. /.netlify/functions/my-test-function. Seems to work.