This page outlines some of the LMS prerequisites needed before LTIAAS can be tested and used with an LMS.
1. A publicly accessible domain name
LTIAAS uses the internet to send and receive messages to the LMS. This requires LMSes to have publicly accessible domain names. If you are hosting an LMS on a personal machine (i.e. your laptop), that is not accessible from the internet, LTIAAS will not work.
The best option to access an LMS, even for testing purposes, is to host one properly on the internet. If this is not an option, you maybe be able to use the ngrok service to expose a private machine to the internet for testing purposes.
The LTI protocol relies in HTTPS for security. LTIAAS will refuse all insecure connections to LMSes. If an LMS doens't support HTTPS, if an SSL certificate has expired, or if an SSL certificate is self-signed, the connection will be denied by LTIAAS.
Let's Encrypt is a good resource to generate trusted SSL certificates for free.