Earlier quoted context omitted.
The interface between Lambda and your business logic is usually very thin so in case of simple REST APIs migrating from platform (as long as the target platform has a compatible language runtime) to another or to be executed in a web app framework is rather easy. Serverless applications' reliance on other proprietary services like Cognito, DynamoDB etc is another thing however...
The problem is also that Lambda works really poorly with anything that is NOT Cognito and DynamoDB. For example, we were using some CouchBase we deployed ourselves - however, that meant that the Lambda now had a network interface in a private subnet, and start times skyrocketed, especially for concurrent access. When we also started doing our own authentication with yet another Lambda, request times for cold lambdas…