I agree the lag does not appear to be constant, and does vary, and may not explain everything, however, someone
earlier dismissed the lag between temperature and CO2 as irrelevant, so I made some simple
calculations, and surprised myself, in that (possibly) co-incidentally the lag of roughly 800 years + / - 200 (my own estimate),
matched the time between the MWP and the start of Industrialisation, where CO2 levels are said to start rising, of course it's a very rough estimate.