Api Gateway IAM Policy update took some time reflect causing 500 error due to missing permissions to invoke Lambda

While upgrading to CDK v2, we have updated our CLE lambda alias name from live to Live to avoid resource creation conflict errors during deployment. We have updated our smithy model to change alias name in our Api gateway integration with our Coral Lambda.

After this change we deployed the code to beta, Post and Get requests started working fine after sometime. But it took almost 15 minutes for the API gateway to successfully invoke the lambda for Patch operation.

The error I got was, Execution failed due to configuration error: Invalid permissions on Lambda function. I checked the IAM permissions for Api gateway and I saw that policy was updated. So, don't know why this happened. We can't risk it in the Prod. Please let us know why it happened.