You can disable specific menu entries by placing a JSON file in right format into a pre-defined location. The JupyterLab user interface is fully customisable by JSON settings; you can pre-define the settings for your users by placing per-package settings in overrides.json file in the appropriate location.
This is documented in JupyterLab documentation, in the User Guide → Interface Customization → Context Menu section:
https://jupyterlab.readthedocs.io/en/stable/user/interface_customization.html#context-menu
and more in depth in:
https://jupyterlab.readthedocs.io/en/stable/extension/extension_points.html#context-menu
The overrides.json file is documented in User Guide → Advanced Usage:
https://jupyterlab.readthedocs.io/en/stable/user/directories.html#overrides-json