I suspect the problem might be with how JupyterLab uses just the domain name (?) to identify different deployments. This normally works since you’ll normally only have one server running on a host:port but fails with mybinder.org since you can have multiple independent JupyterLab instances.
For instance, if I go to http://mybinder.org/v2/gh/binder-examples/jupyterlab/master?urlpath=lab/tree/index.ipynb it works, but if I launch that link again it’ll launch a second mybinder.org server, but I’m sent to something like lab/workspaces/auto-6. This is similar to what happens if you open another tab for the same single JupyterLab server, e.g. http://localhost:8888/lab vs http://localhost:8888/lab/workspaces/auto-y