You can configure the AWS Codebuild jobs to send the logs to S3 bucket as shown in the below snippet
And from there you can configure your S3 Events Notification and hook your lambda to that.
As far as I read the docs there are three methods of authentication to codecommit and only one provide a related solution to getting the email address of the code committer via sessions tags.
So you are left with Authorization based on CodeCommit tags which is recommended for
If you want to connect to CodeCommit using a root account, federated access, or temporary credentials, you should set up access using git-remote-codecommit
You need to connect pieces together here Monitoring CodeCommit events in Amazon EventBridge and Amazon CloudWatch Events
Because as soon as the code commit's event gets triggered with the information( provided you are using GRC), you need to wait for the code build job finishes which puts your jobs' logs to s3, and eventually your lambda gets triggered.
I will use AWS Step Function Parallel Workflow for this where the event from the codecommit triggers the lambda and then Step function Code Build works do the rest for me. But this is just a choice, you handle the integration via lambdas as well.