Lung CO2 concentration as a function of Dive time?

Well, you surely know all this, but just for the reference: there are several reasons for the low CO2 level - at deep dives it is the partial alveolar pressure of CO2 - already in moderate depth it grows significantly, preventing so diffusion of CO2 from blood to lungs. Second reason is vasoconstriction reducing the blood circulation and consumption of oxygen in muscles, so the CO2 or lactic acid produced by the metabolism will buffer in the tissue and body liquids (not only the blood). Then of course, the switching to the anaerobic metabolism producing lactic acid instead of CO2 is another (though related) factor.

I do not remember seeing any document specifically studying the CO2 level and observing the effects exactly as in the quote you mention, so cannot post any data confirming the claim exactly. Some hints may be in the following documents. I do not have access to the full versions, so cannot tell for sure, but from the titles and the abstracts it is apparent CO2 production or retention are studied in more details there.

Hypoxia and carbon dioxide retention following breath-hold diving -- Paulev and Naeraa 22 (3): 436 -- Journal of Applied Physiology
Tissue oxygen and carbon dioxide stores and breath-hold diving in humans -- Liner and Linnarsson 77 (2): 542 -- Journal of Applied Physiology

Also some of the other documents linked at the bottom of those pages may bring some more info about the CO2 levels during a breath-hold.

I think that when they write CO2 remains constant during a surface apnea, it rather means that it climbs to a certain level and then only changes very slowly (or better told - climbing along a logarithmic curve). It certainly does not mean it remains on the same level as at the beginning of the breath hold, as someone could have interpreted the partial quote. I agree that It would be interesting to know what is behind it exactly. Yes, the retention in tissues due to the dive response is certainly the main factor, but there is likely more behind it. Perhaps higher affinity of CO2 to the hemoglobin in progressing apnea is another factor. And the CO2 dissolved in blood (not bind to hb) perhaps needs a higher gradient to start dissolving into lungs. And the small pressure change in lungs when laying in water, although just on the surface, may play a role too. I guess there may be up to around 5% pressure increase (the diaphragm can be up to roughly 50cm under water) and another couple of percent of pressure increase may come from packing.