Sounds like you hit the same wall as myself doing the exact same thing. App review isn't necessarily needed, unless random users login and administer it via the Facebook accounts? If not, follow the video tutorial for Lead Ads Webhooks to setup the webhook.
After this is done though it still won't send leads from the Facebook App because the Facebook Page needs to subscribe to the app for this to happen (but now tests can be sent at least). The subscription API documented here should help with this (note that GET requests list the subscriptions and POST requests add new ones as it's RESTful).
Even after this it still won't be enough to get this setup though. The Lead ID will come from the webhook API, but not the actual user information. To do this I suggest downloading the Facebook Ads SDK and using the Lead class along with the ID to get the information. Prior to this though it might be useful to create a lifelong token that the SDK can use to access the Facebook Page via by creating a System User whom the access is given (not that this shouldn't be viewable by users!). Remember to give appropriate permissions and assign appropriate assets (also with appropriate permissions).
