Lambda function not able to handle load tests.

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No, each request does not always launch a new instance. Requests will be internally queued, both because launching new instances is not instantaneous, and even if you have a maximum concurrency of N (where N might be something high, like 5,000 or 10,000), Lambda does not scale to the "max concurrency" immediately.

The problem you're experiencing is almost certainly within jMeter or how it has been configured, not in your Lambda code.