Lambdas & Cobol: yes, we can!
The benefits of serverless architecture are not reserved to greenfield / new applications. Cobol code can also leverage the advantages of Lambda functions on AWS. See my last Github Workflow automating the deployment of a Cobol-based Lambda function if you want to see how it's possible.
https://github.com/didier-durand/lambda-cobol
Just replace the Python's snakes by Cobol here above to understand what's you'll get with this repo.
It's made to be forked and extended. So, happy hacking!