In World of Thedas it says that mages should not get close to raw lyrium as there is a risk of death from internal haemorrhaging, quiet apart from the likelihood of it sending them mad. I'd already picked up on the fact that all the mages in our party should have been freaking out in the Descent with all that lyrium flowing around. Then again, just a small bit of red lyrium sent Bartrand and Meredith mad, yet it is all over the place on the surface, with no one suffering any ill effects.
That poor Templar in the prison in DAO was in a terrible state through lyrium withdrawal, so Cullen must have had a real strength of mind to have been able to kick the habit and still be able to operate, considering he must have been on the stuff for years, but that can be the case with addictive substances. Some people are able to kick the habit more easily than others.
The Templars did seem to have lost something of their abilities since DAO. Back then they were able to affect your companion mages with the comparable skills that your PC/Alistair had as a Templar. However, the same was true of enemy mages both in DAO and DA2. I always made a point of hitting them as quickly as possible before they could let off their spells against my party, particularly blood mages. Whereas I stopped worrying about the opposition mages in DAI because I really didn't find their spells that troublesome. It was ironic considering we were being opposed by the Venatori, the majority of whom came from Tevinter and therefore should have been controlling the minds of my companions and inflicting all manner of pain with their blood magic.