Well as said the CO2- d18O (dD) proxies in their shapes show a very tight relationships if we shift scales a bit like http://home.wanadoo.nl/bijkerk/EPICA3.GIF .
But system response of higher order semi linear close loop feedback systems with substantial lag is completely different and most certainly not a lateral lagging duplicating echo of the apparent input.
System response examples here. That's why there should also be engineers in the climatology branch.
How about the time scale? In Greenland it's simple, the annual ice layers clearly show. But Antarctica this is not so, due to the low accumulation rate. At only a moderate depth in the core the annual layers merge under the gigantic pressure of the overlaying ice. So, instead, a multitude of tricks is used to establish dating, like tuning 10Be spikes of known ages or dated tephra layers etc giving a few odd hard dating points but how do you wiggle the rest in between?
I believe that the strong correlation between isotopes values and layer accumulation seen elsewhere in Greenland, is used as a given to reconstruct the dating in between.
But when the annual layers still can be counted in the upper part of the EPICA ice core some 5000 years, we see a good but far from ideal 100% correlation:
http://home.wanadoo.nl/bijkerk/epica4.GIF
Blue is annual layer thickness relative to the trend (detrended), red is dD isotope permil values also relative to the trend.
(incidentally, notice the Medieval Warm Period and Little Ice age perfectly showing in the last 1300 year)
So the assumption of 100% correlation between moisture and isotopes, used to calculate layer thickness will introduce a dating error.
The second big problem is the ice age - gas ice difference as initial open snow /ice at the surface permits air to diffuse in, refreshing the old captured air. Consequently, in the open phase (firn), the first 80-100 meter, the air is much younger than the ice. Typical for Antarctica summit domes is 1000-5000 years. it goes without saying that establishing the correct gas age (matching all kind of spikes) also causes errors.
Seeing the near identical shape of both isotopes and CO2 graphs and taking into account system response characteristics, my guess is that both are simultaneous reactions to another cause and the lagging is simply artefact due to erroneous assumptions.