Forum Discussion
Red lyrium of varying strengths can be found throughout the game, generally anywhere where Red Templars can be found (not sure if siding with the Templars changes the availability of red lyrium). Pure red lyrium (the strongest type) can be found most often in Emprise du Lion, both during the quest to overtake the castle there, and after rebuilding the bridge during the quest to claim the towers. You might also get some on the Storm Coast after the Red Templar stronghold opens up (should be a war map mission of some type, I'm not sure exactly when it becomes available).
If you have Trespasser, you can buy as much red lyrium as you want from a merchant at the Winter Palace. Not much use for the main game, but there you go. 😛
If you sided with the mages, EDL, SC, EG all good places to get red lyrium. Just kill red Templars.
If you sided with Templars, then you've got a lot of mages and not so many red Templars but SC and EDL still has them.