This was asked and answered a while ago, but having just thought about this myself, I thought I'd add an approach.
As mentioned, Event Sources may be the best bet here. Alternatively, and I haven't tested this nor thought this through (so this is kind of academic), but it may be possible to accomplish this via a Fan-Out pattern with SNS as follows:
1. Create a SNS topic.............................: SNS-topic-01
2. Subscribe a SQS queue to that topic............: SQS-queue-01
3. Subscribe a Lambda Function to that topic......: LAMBDA-func-01
Using this configuration, submitting a message to the SNS topic will enqueue it to the SQS queue while simultaneously triggering a companion Lambda function. That Lambda function would be written to read that very same SQS queue but with Long Polling enabled (up to 20 seconds) so that it doesn't read the queue before the enqueue completes (i.e. race condition).
In essence, this scheme just-in-time invokes one Lambda function for each enqueued SQS message. I don't know how simultaneous Long Poll readers work on SQS (... does one get dropped?), but this is just another way to consider solving this. =:)