Capacity indicates the amount an object can hold, thus the units for capacity are the same units as for volume. The SI unit for volume is the liter, so we measure lung capacity in liters.
Centimeters are a measure of length. If we needed the diameter of a lung we might use centimeters. We would use square centimeters to measure the surface area of the lung.
We could measure lung capacity is cubic centimeters if we thought of measuring the space within a lung as opposed to the amount (volume) of gas contained in the lung. However we are interested in the volume since we are more interested in the function of the lung (taking in air as a gas) than the amount of space it takes up in the chest cavity.