And let's just assume that the CO2 lag, as you stated, is real. (And just so you know the lag amounts in your studies were proven to be based off error -- a better estimate would be roughly 200 years in lag)

https://www.scientificamerican.com/article/ice-core-data-help-solve/

Anyhow back to the point I'm going to make. The data taken from your studies was taken how long ago again? One says the sample dates back 420,000 years ago. Now unless I have everything wrong about inventions and the way society -- or lack thereof because humans didn't exist -- I don't think there were the same amount of CO2 sources as there are nowadays. Now what does this mean? Yes, the global climate changed and warmed in years past due to other events, thus increasing CO2 due to melting of ice and the release of more CO2 into the atmosphere. 

What your studies neglect is any reason. They pull out a piece of data and champion it yet don't recognize the scientific relevancy of the actual data