How does lung volume control inspiration?

An increase in volume DECREASES the pressure in the chest (pressure and volume vary inversely when temperature is held constant -- Boyle's law). Gas can only flow from an area of higher pressure to an area of lower pressure. It can't go uphill -- ever. It can only go from high to low pressure. When the diaphragm and intercostals contract, the diaphragm flattens and the rib cage rises. That increases the volume of the chest. That increase in volume decreases the pressure inside the chest (temperature is held constant -- because the temperature of the chest cavity does not change appreciably. It remains at body temp.). Air then flows from the area of higher pressure (atmospheric) to lower pressure (intrathoracic). That continues until the pressures are equal.

When the diaphragm and intercostals relax, the chest cavity decreases in size, the pressure increases to above atmospheric, and gas flows again from the area of higher pressure (intrathoracic) to lower pressure (atmospheric) until they are again equal.

It has nothing to do with the concentration of oxygen. You can ventilate a lung with ANY gas. It has to do with the change in pressure and only the change in pressure -- which is a function of the volume of the chest cavity.