^ Lyrium is used to augment a mage's own power for really big spells. Similarly, blood magic, and the amount of blood used (hundreds of slaves to enter the Golden City) does the same.
There are two examples of this stated in the games that I can recall at the moment. The first is in DAO when you go to the mages for assistance with Connor. When you return to the castle, Irving mentions having brought lyrium and extra mages. The second is in DA2 when you learn about Merrill's use of blood magic shortly after meeting her. She says, "If I had piles of lyrium lying about I could have used that."
The whole thing in these games with mana as a power source for mages, and how that applies to the lore aspect of it, has always been really thin to me. The official codex explanation of mana is, "a measurement of one's ability to draw power from the Fade." Forgetting game mechanics for the moment, how is an individual's mana level measured??
The entire codex is Mana and the Use of Magic.
Mana is that which defines a mage. It is potential that dwells within a person but does not always manifest itself. All men are connected to the Fade; we go there to dream. But only those with this potential may draw upon its power. Mana is, then, a measurement of one's ability to draw power from the Fade, and it is this power that is expended in magic.
As in all other things, it has limits. Just as a man has the strength to lift only so much weight and no more, a mage cannot work more magic at one time than his mana allows. If he wishes to work magic that would be beyond his strength, a mage must bolster his mana with lyrium. Without lyrium, it is possible for the reckless to expend their own life-force in the working of magic, and occasionally, ambitious apprentices injure or even kill themselves by over-exertion.
--From The Lectures of First Enchanter Wenselus
I've never been able to reconcile the lore explanation of mana with the game mechanic of mana as a power source in my own mind. In the game, mages drink lyrium potions to replenish mana, but the lore suggests that lyrium potions should instead prevent it from being depleted, increasing our reserves.
I think ideally, to meld the lore with the gameplay, the implementation of lyrium potions would work like so. The mage class would have a smallish, fixed mana pool, let's say of 100 mana. Most minor spells would cost < 100 mana and mana would regenerate naturally over time. That's all fine. But really BIG spells would cost > 100 mana, say 110, 125, etc, depending on the spell. In order to use those spells, the player would have to think ahead and take a lyrium potion to temporarily increase their mana pool in order to cast The Big One. Lyrium might also have diminishing returns over time, so the first time you use it you gain +50 mana, the second time is +40, and so on. This would reflect the natural build up of lyrium resistance in the mage and also prevent the player from casting The Big One too often.
To keep it fun, the cooldowns, hidden and visible, on all of these things would reset once combat is over, so you don't have to worry about saving your lyrium just for boss fights. Or alternately, it might actually be more realistic to require the player to save these large and costly spells for boss fights, but I think that can lead to gameplay that makes these spells feels less fun if you're hoarding them "just in case." For example, I hardly ever use DAI focus abilities while I'm out in the world and do typically save them for boss fights or really difficult rifts.