mcrittenden is right in that it probably will cost more to run than just having the old processes run on ECS/EC2. Lambda charges a premium for maintaining its control plane and development of the product that only makes sense to pay if your app has 'idle time'.

But also there is a per account per region concurrency limit of 1000 parallel executions. That's shared across all lambdas. If you hit it, requests will not be for-filed, increasing this limit is entirely at Amazons discretion, and wont they necessarily do it. I stand corrected, see comment.

https://docs.aws.amazon.com/lambda/latest/dg/limits.html

In your case 3m reqs/min will be fine if each request can be completed in no more than 20 milliseconds, and then you'll be on the knife edge.

If you wanted to reap the benefits of Lambda on the development side, loose the limits and keep server costs low(er) you could deploy OpenFaaS or similar in ECS. However you then loose the operational benefits of a managed solution.