"There hasn't actually been any global warming for the last fifteen years or so"
Assertions like this without any reference to data have to be suspect.
NASA has comprehensive climate data readily available and there is pretty good transparency on where its from and how its been processed.
It is here: http://data.giss.nasa.gov/gistemp/
If we just look at the annual global "anomalies" - (anomaly here is defined as the amount that that year's value differs from the overall mean of the data set) the continually rising trend to 2015 is fairly clear.
There is significant fluctuation (roughly +/- 0.2 of a degree) year on year. One of the simplest means of smoothing them out is to use a moving average. Using a 5 year window the trend is even clearer, all the averages of 0.6 or higher occurred since 2005 and the highest two - of 0.712 and 0.702 are 2014 and 2015.
However what is visible is that the trend seems to slow at around about 2005-2006. By eye there is a "knee" in the trend line. Its still upwards but at a slower rate. From 1970-2001 the average rate of increase in the moving average is 0.016 degrees a year, from 2002 to 2015 the rate is 0.011 degrees a year (*). It is not clear that that rate is declining further however. Perhaps it is this reduction in the rate of the rise that Lewis confuses with a stall in the rise itself.
(*) even using the moving averages these rate figures do vary somewhat on the exact start and end year used.