From the AWS Lambda FAQ:
Q: Is there a limit to the number of AWS Lambda functions I can execute at once?
No. AWS Lambda is designed to run many instances of your functions in parallel. However, AWS Lambda has a default safety throttle of 100 concurrent executions per account per region. If you wish to submit a request to increase the throttle of 100 concurrent executions you can visit our Support Center, click “Open a new case”, and file a service limit increase request.
Q: What happens if my account exceeds the default throttle limit on concurrent executions?
On exceeding the throttle limit, AWS Lambda functions being invoked synchronously will return a throttling error (429 error code). Lambda functions being invoked asynchronously can absorb reasonable bursts of traffic for approximately 15-30 minutes, after which incoming events will be rejected as throttled. In case the Lambda function is being invoked in response to Amazon S3 events, events rejected by AWS Lambda may be retained and retried by S3 for 24 hours. Events from Amazon Kinesis streams and Amazon DynamoDB streams are retried until the Lambda function succeeds or the data expires. Amazon Kinesis and Amazon DynamoDB Streams retain data for 24 hours.
What constitutes 'reasonable bursts' above? Does anyone have specific numbers?