Using AWS Lambda is exactly what we’re doing for the Hearthstone Deck Tracker Extension. You can find our EBS source code here if you’d like to check it out for reference.
We’ve had a good experience with it for our EBS so far, but there’s a few smaller caveats to be aware of, such as keeping the lambda warm (we use Zappa’s keep_warm that basically cron’s it every 4 minutes).