Deliver logs in JSON to CloudWatch

It would be very nice to have the logs published to CloudWatch in JSON format (for example, such as: https://docs.aws.amazon.com/lambda/latest/dg/java-logging.html). Otherwise, it is very hard to sort through them.

This is somewhat related to #226.

If we find a nice way of logging which brings the most (useful) information as possible, other language plugins can adopt it.