How to handle authorization for a non-user based Laravel API? - development

How to handle authorization for a non-user based Laravel API?

I have a Laravel web application for a restaurant with its own user base.
I have another web application for a bookstore with its own different user base.

I would like to create a third application (mostly API, probably using Lumen) that can create accounting records from both the restaurant and the bookstore on every transaction that is made (i.e. when I sell any food, make a POST request to this API to insert a record, and do the same if I sell a book).

How can I guarantee that only authorized users from my web apps (any user) can make requests to my API, without asking them for any additional password?

from Laravel Questions and Answers https://laravelquestions.com/laravel/how-to-handle-authorization-for-a-non-user-based-laravel-api/
via Lzo Media