How do you extinguish the braziers [lever puzzle] in High Gate Ruins?

As luck would have it, Lydia and I just pulled up to these ruins, so I can share some first-hand experience.

Anska was just inside and she helped us out with the draugr, in return for finding a scroll belonging to some old guy.

If the same happened to you - and Anska was there on your first visit - perhaps the braziers are somehow linked to her quest, meaning if you can't re-do the quest, you can't re-do the ruins? Or perhaps they're tied to the murder of the aforementioned old guy?

A bug listed against the quest 'A Scroll for Anska' on the Elder Scrolls Wiki would seem to concur, as it indicates that this dungeon can only be completed once:

The quest must be completed the first time the dungeon is entered, as it is not possible to return later. The dragon priest does not respawn, and the only way to open the gates on either side of his tomb is to kill him. They close after leaving the dungeon for the first time.

However, that same list of bugs suggests a possible, although slightly convoluted, workaround:

It is possible to re-enter the dungeon through the back entrance to Vokun's Throne room. It is necessary to have a follower other than Anska to succeed. Climb on top of the ruins on the opposite side of the back entrance to Vokun's Throne room. Then jump down on the little square surface, which is level with the opposite side. Then use Whirlwind Sprint (use the full shout if to be sure). Wait by the gate, the Follower should come to the other side of the gate. Then ask them to pull the chain, and entry will be possible.