Asynchronous lambda invocation allows for a quick response back (e.g. 202 Accepted) while allowing the lambda to continue running. This would be desired if you wish to kick off a lambda that runs longer then the API GW 30 second timeout, or if the application needs a quick response without the need for direct success for failure of the longer running lambda.
At the time of this post this feature is not natively supported by serverless framework, but it looks trivial to set it up via a resource override. More information at https://github.com/serverless/serverless/issues/4862
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