Strictly speaking, purely in terms of the question of processing the gases involved, no changes are needed to human lung physiology to process carbon dioxide. They already do process it; it's just that it's a waste product to be expelled, rather than a 'raw material' to be taken in.
The challenge is really to come up with a physiological modification that allows the $\require{mhchem}\ce{CO2}$ to be substituted metabolically for $\ce{O2}$. At a high level, oxygen is the final electron acceptor at the end of the electron transport chain (link modified from the original):
The final acceptor of electrons in the electron transport chain during aerobic respiration is molecular oxygen although a variety of acceptors other than oxygen such as sulfate exist in anaerobic respiration.
Interestingly, carbon dioxide is known to be an alternative electron acceptor in certain methanogenic bacteria (emphasis added):
Methanogenesis in microbes is a form of anaerobic respiration. Methanogens do not use oxygen to respire; in fact, oxygen inhibits the growth of methanogens. 279
The terminal electron acceptor in methanogenesis is not oxygen, but carbon. The carbon can occur in a small number of organic compounds, all with low molecular weights. The two best described pathways involve the use of acetic acid and inorganic carbon dioxide as terminal electron acceptors:
$\ce{CO2 + 4 H2 → CH4 + 2H2O}$
So, somehow you have to genetically engineer your Martian explorers to "eat" (inhale?) hydrogen, which their bodies then "burn" with atmospheric $\ce{CO2}$ to form methane and water, while releasing energy. You could catch their exhaled methane to use as, e.g., vehicle fuel, but you'd have the same no-oxygen-around conundrum as what causes breathing problems for us unmodified humans.
For interest, that above reaction of carbon dioxide and hydrogen is called the Sabatier reaction, which is in active use on the International Space Station as a method for processing exhaled $\ce{CO2}$ and recovering water. The methane generated there is apparently just vented into space, but the same sort of reaction is being investigated (NASA pdf link) for actual Mars missions, as a potential source of fuel, generated from solar power and local carbon dioxide. 279