I think Lambda is a great idea. They are stateless which means very cost-effective, but also you’d need to implement one of the persistent data stores for your Tracker implementation, and, almost certainly, the custom one, connecting to DynamoDB. I’ve not seen any code immediately around that does this but it would be very useful.
Also, the default lambda behaviour is that the first request boots up a VM temporarily and keeps it around for about 10 minutes. So the first user of your service (be it human or a bot) will be 6+ seconds. The most efficient solution is almost certainly provisioned concurrency that keeps things warm for you at a slight increase in price. Very cool stuff.