You can write move complex lamda with aws step functions. Even lamda functions can fire child lamda functions. But you must remember that you will be charged more for lamda than time on some ec2 machine. So it does not make sense to run log running processes on lamda IMO.
For me lamdas is event driven design that glue some long running services (your services or AWS services)
Cloud computing requires to not only treat containers but also servers like “Cattle”
What would happen if someone kill your server and you lost all your state?
The History of Pets vs Cattle and How to Use the Analogy Properly | Cloudscaling 
12 factor apps
VI. Processes
Execute the app as one or more stateless processes
PS
Interesting article about cost
