The template provisions a working stack to store the AWS IP ranges JSON file in a S3 bucket using AWS Lambda.
To verify or check errors in cross-account SNS notifications you will need two AWS accounts. The basics for how to set up cross-account notifications are described in the AWS Lambda developer guide example "Using AWS Lambda with Amazon SNS from Different Accounts".
In addition to those steps you need to enable delivery status on the topic. Delivery status is sent to AWS Logs in log groups with the name sns/[REGION]/[AWS ACCOUNT ID]/[TOPIC NAME] for success and sns/[REGION]/[AWS ACCOUNT ID]/[TOPIC NAME] for failure.