I’m not sure if I understand your question correctly. All types of masonry chimneys (stone, brick, cinder block, etc.) currently require liners, but they do not require stainless steel liners. On the other hand, some of the gas burning appliances require stainless steel vent pipes, and if such appliance discharges through the masonry chimney, stainless steel liners. So, it’s the matter of matching the appliance’s venting requirement.
In other words, if your natural gas furnace (or boiler) requires stainless steel vent pipe (most likely due to acidic condensation) and if you have a masonry chimney, you need to install a stainless steel vent connector between the furnace and the chimney, install a stainless steel liner inside the chimney
to prevent its deterioration, and connect both in such way that it prevents condensate leakage inside the chimney.