It is stateless in that sense. To run your lambda, there needs to be zero things in memory, unlike a traditional express/django/rails or other non-serverless apps.
If your lambda involves persistent storage, your testing might want to wipe or prepopulate the DB with some objects first, but that's not hard and doesn't add complexity, and as mentioned you don't need anything in memory.
If your lambda involves persistent storage, your testing might want to wipe or prepopulate the DB with some objects first, but that's not hard and doesn't add complexity, and as mentioned you don't need anything in memory.