Lung capacity of a centaur might help in doing strenuous work at altitude, but there are two biophysical limits that cannot be overcome by just increasing lung capacity.
Lungs are basically a semi-permeable membrane that allows gases to pass through. Oxygen moves from air to blood because the partial pressure of oxygen (ppO2) dissolved in the blood in the lungs is lower than ppO2 of the air in the lungs. Carbon dioxide moves the opposite way because its partial pressure (ppCO2) is higher in the blood than in the air, because the blood brings more CO2 into the lungs all the time. But there is nothing to stop the gas exchange from going the other way if the partial pressures change, or to force it to happen if there is no sufficient difference of partial pressures.
There's also some water vapor, which always stays at or above certain minimum partial pressure (ppH2O) by the physiology of the lungs: if the air you breathe is drier than that, some water will come out of your blood and so you'll lose moisture on every exhalation.
And finally, there's the partial pressure of nitrogen (ppN2), which is important for scuba diving, but in aviation it basically just takes up space from the important gases (unless you're flying soon after scuba diving, in which case you'll need to be careful).
As altitude increases, the ambient air pressure decreases, and the partial pressures of the various components of the ambient air decrease in the same ratio. 279
But in your lungs, the carbon dioxide and water vapor exiting the blood will keep the partial pressures of these components of air at or above a certain minimum level. Basically, when you reach the point where the sum of partial pressures of ambient nitrogen + carbon dioxide in the lungs + water vapor in the lungs equals the total pressure of ambient air, the flow of oxygen from air to blood will be completely blocked. You can breathe all you want, but you aren't getting any oxygen in.
If there is any remaining oxygen in the blood, it will actually escape if the ppO2 in the air is lower than the ppO2 in the blood. This a big part of the reason why a sudden depressurization in a pressurized aircraft at altitude makes you pass out so quickly, and also why the safety instructions in passenger airplanes tell you to always put on your own oxygen mask first before helping others.
(This is why mountain climbers talk about the "death zone" near the peak of Mount Everest and other tallest mountains: if you are near the top of Mount Everest and not using supplementary oxygen, you will be effectively suffering from a constant oxygen shortage because you're approaching this limit.)
By using supplementary oxygen at ambient pressure, you'll effectively replace the useless nitrogen component with more oxygen, which will allow you to go higher.
But once you go high enough, the sum of partial pressures of just the carbon dioxide and water vapor in the lungs (which have a minimum limit set by physiology) will equal the total pressure of the ambient air at altitude, and then you'll have the same problem again, and supplementary oxygen will no longer help. At that point, you will need either a pressurized cockpit, or a spacesuit.
(Source: an aeromedical lesson that was part of glider pilot basic training.) 279