If you’re using a recent enough version of JupyterHub, you can use the experimental telemetry / eventlogging system to capture user server start and end events. This can then be used to see session lengths, etc. If you have a persistent hub PVC that is storing the sqlite database, you can put the telemetry there with a FileHandler. Just make sure the PVC is big enough 
There is a PR in notebook itself that should provide more events, but I don’t think you need those.
I probably also have some scripts that can parse jupyterhub logs to emit conformant Telemetry logs. Let me see if I can find those.
Hope this is useful!