No. Heat, food exposure and the rail's design make an ordinary household lubricant an unsuitable assumption.
What the observation means
Stiffness may follow residue, cleaning damage or a mechanical issue. Adding oil can conceal the symptom while creating odour or smoke during later heating. The owner's guide may permit a specific cleaning method, but that is different from lubricating internal bearings yourself.
A useful next step
Leave the affected rail unused if its movement is unreliable and check the manufacturer's care guidance. Describe whether one side or both sides bind and whether this began after cleaning. Do not dismantle the rail or substitute grease selected only by its advertised temperature rating.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.