When is it not appropriate to use serverless technology such as AWS Lambda?
There is likely no general answer to this question, but some reasons to not consider Lambda (or other serverless platforms) include:


App requires a language which is not available (C++, Haskell, Erlang, etc.)
Organization has existing substantial investment in containerized (or other) app development model, including developer knowledge, build and deployment pipelines
Portability is concern; i.e. the organization wants/needs to keep app in a state which is portable across platforms (AWS, Azure, various k8s implementations, and so on).
Cost. Do costs of running the Lambda function(s), as well as associated resources (API Gateway, VPC components) exceed budget? This is unlikely if the org. is already running in AWS, but can be a factor when compared against existing (and paid-off) on-premise resources.