Do not pour lubricant or cooking oil into the disposer as maintenance. Owner care should follow the model's instructions, and adding oil to the water path is not a general remedy for noise or a stiff mechanism.
What the observation tells you
The moving parts you cannot see are not made accessible for lubrication simply because the appliance has a sink opening. Spraying a product through that opening can introduce an unsuitable substance without reaching the cause of a fault. Keep grease out of the drain.
A useful next step
If the appliance sounds dry, rough or strained, describe that observation to an engineer. Do not substitute a lubricant experiment for proper assessment.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.