Invoke lamda async from Aurora PostgreSQL

Calling Lambda from Aurora PostgreSQL is not yet supported. Rather than calling a lambda function in a trigger, you can consider consuming the change stream from PostgreSQL in a lambda function. See: https://aws.amazon.com/blogs/database/stream-changes-from-amazon-rds-for-postgresql-using-amazon-kinesis-data-streams-and-aws-lambda/

Think about the architecture and volume. Do they want to see every change, or only changes on a certain table?

How many changes per minute are they expecting?

If they are looking for the all changes or a high volume of changes, they may prefer using a small EC2 instance and a CDC tool like Debezium which can consume CDC records from PostgreSQL and publish to various targets. See: https://debezium.io/blog/2020/02/25/lessons-learned-running-debezium-with-postgresql-on-rds/ or: https://aws.amazon.com/blogs/apn/how-behalf-met-its-streaming-data-scaling-demands-with-amazon-managed-streaming-for-apache-kafka/

This feature was launched in December 2020: https://aws.amazon.com/about-aws/whats-new/2020/12/amazon-aurora-postgresql-integrates-with-aws-lambda/