There isn’t yet any empirical evidence for their claim that greenhouse gases even cause temperatures to increase.
Lindzen accepts the main principle of the greenhouse effect, that increasing greenhouse gases (like CO2) will cause a radiative forcing that, all other things being equal, will cause the surface to warm. He uses an odd measure of its effectiveness though, claiming that a doubling of CO2 will lead to a ‘2%’ increase in the greenhouse effect. How has he defined the greenhouse effect here? Well, a doubling of CO2 is about a 4 W/m2 forcing at the tropopause, which is roughly 2% of the total upward longwave (LW) (~240 W/m2). But does that even make sense as a definition of the greenhouse effect? Not really. On a planet with no greenhouse effect (but similar albedo) the upward LW would also be 240 W/m2, but the absorbed LW in the atmosphere would be zero, so it would make much more sense to define the greenhouse effect as the amount of LW absorbed (~150 W/m2). In which case, doubling of CO2 is initially slightly more*, but as soon as any feedbacks (particularly water vapour or ice albedo changes) kick in, that would increase.