Using a load balancer, you would have to account for the time to launch and instance. It would probably make your solution a bit more complicated than it needs to be. Instead you may want to consider the following.
You have an instance that receives requests. If its not a lot of requests, it could even be a micro instance. This instance would then create jobs within SQS. (You could use another message queue system, but SQS metrics can be used in autoscaling).
Your worker instances would take a message from SQS and then process it. You would save the results to s3 or database depending what is best for your scenario (You may be able to deliver the results to a callback provided by the client).