Create an Amazon Simple Queue Service (Amazon SQS) queue and set it as the dead-letter queue for the API.

Establish two Amazon Simple Queue Service (Amazon SQS) queues: a primary queue and a secondary queue, with the secondary queue acting as the dead-letter queue for the primary. Modify the API to integrate with the primary queue and configure the Lambda function to be triggered by messages in the primary queue.

Set up two Amazon EventBridge event buses: a primary event bus and a secondary event bus. Update the API to direct data to the primary event bus. Create an EventBridge rule to handle all events on the primary event bus, targeting the Lambda function, and set the secondary event bus as the destination for failed Lambda function invocations.

Develop a custom Amazon EventBridge event bus and configure it as the destination for failed Lambda function invocations.