OP, this is whats been bothering me since DA2. Frankly, the only reason the Templar Rebellion is still active is because of the extremely convenient Red Lyrium and because Bioware REALLY wants a Templar enemy in Inquisition. But I can understand that.
Practically everything the Templars have, it comes from the Chantry. Logistics, food, equipment, money, and lyrium. And then they cut themselves off from Chantry. And lots of people are under the impression that the Templars have more autonomy than they think.
Money to buy lyrium? How?. Their income source came from the CHANTRY. Whatever money they have it should be drying up by now. Where are they supposed to get more money? Mercenary activities since Templars are soldiers? That would divide their forces away from fighting mages. And why would anyone hire them since they would be logically too expensive, especially needing lyrium to function?
Smuggle lyrium? There is no freaking way smuggling should be able to support all of the Templars. Smuggling requires money, money came from the Chantry, and the Templars cut themselves off from the Chantry. And not every trader will want to deal with them. And whatever money the Templars have, how the hell do they expect to compete with the Chantry who can simply outbid them? And then store the lyrium back in Orzammar for safekeeping? The whole point of the Chantry's monopoly on lyrium was to make it very difficult for the Templars to disobey them. And make them crawl back and beg for another dose before withdrawal
Raid the Chantry lyrium stores? They're not gonna freaking last forever. And good luck with losing further Chantry and public support.
Mining lyrium? *sigh* Even if the Templars somehow found an independent source of lyrium, did you forget that raw lyrium is dangerous to humans? And that only dwarves can successfully mine it?
But again, this is all moot, since the existence of Red Lyrium.