JupyterHub doesn’t control any of the UI once users are running in their environments. It launches either JupyterLab or classic notebook, so it is the same for JupyterLab, whether run inside or outside JupyterHub. If you want to make sure JupyterHub launches with JupyterLab, you can set config:
c.Spawner.cmd = ["jupyter-labhub"]
If you are using JupyterHub >= 2.0, this is the default behavior.