Is Lambert out of his mother loving mind? Did he forget that the Chantry controls the lyrium that keeps his Templars sane? WTF is the Lord Seeker doing taking over the Templar Order anyways? They're supposed to be separate brances.
It's not as though there is another viable lyrium source... that... oh. Red lyrium... Sheeeeeeeeeeeeeeiiiiiiiiiiiiiiiiiiiiiiiiiit.
You need to become aware of several things rapidly.
One the Order has deep pockets independent of the Chantry.
Two it has ties to at least two desperate nations/city states's nobility.
Three it was pre annulling in charge of policing the lyrium smuggling trade, it also maintained several connections via the smuggling rings, so it has sources independent of the Chantry.
Four You aware that they were based out of White Spire? Aka the circle of Orlais, aka there is likely a large fortune's worth of Lyrium within, add in what the other fourteen Knight Commanders can bring together and its likely enough to fight this war through to its end several times over.