I believe the lore says only SOME templars have debilitating effects from long term lyrium use. So its not a guarantee like wardens and their taint.
The wiki makes it sound more universal:
In its processed form, lyrium may be handled by anyone, but long term exposure or a single mistake while working with it can lead to serious side effects. Prolonged use becomes addictive, the cravings unbearable. The effects of lyrium addiction for templars include paranoia, obsession, and dementia.[3] Over time, templars grow disoriented, incapable of distinguishing memory from present, or dream from waking. They frequently become paranoid as their worst memories and nightmares haunt their waking hours. Mages have additionally been known to suffer physical mutation.[1]
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All templars are addicted to lyrium, which is officially used to help develop their anti-mage skills and unofficially used as a control mechanism by the Chantry. A lack of lyrium causes the templar to lose touch with reality and suffer from delusions within 1-2 months.[8] The effects of lyrium addiction for templars include paranoia, obsession, and dementia.[9] Over time, templars grow disoriented, incapable of distinguishing memory from present, or dream from waking. They frequently become paranoid as their worst memories and nightmares haunt their waking hours.[10]
It is confirmed that lyrium does have effective benefits for templars, as it builds a resistance to magic in them over time, as well as increasing the effectiveness of their magic abilities, such as being able to shut off a mage's abilities entirely. Some people think that templars are conditioned to be dependent on this mineral for its attributes and that the Chantry knows of its addictiveness. BothAlistair and Evangeline claim that "the Chantry controls the supply of lyrium, and thus they control the templars."[8]