A bit of a nit on the step-by-step rundown of what happens. At step 4 it says the Lambda “dies” but I think this is misleading. The response has completed, but the Lambda has not died. In fact the process is still running which is why the mutable state issue presents.
Even if the process died, the container stopped, and the Lambda went “cold”, I wouldn’t even call that “dead”. It’s just cold. Dead would mean totally failed or decommissioned, I think.