Lemark District

Lemark District is a Burning Quarter dungeon on Losomn. It appears in every world area that includes the Hewdas Clock injectable. You'll need to visit Lemark District before climbing the tower in order to obtain an item required to collect the injectable's reward.

Objective
Solve the house clock puzzle.
Reward
Clockwork Pinion

Lemark District has a fixed layout, so it does not change from roll to roll. It's a very short and simple dungeon, essentially a straight line from the entrance to the objective. Here's the map, which shows the entrance at the bottom:

You enter Lemark District through the arch next to the World Stone checkpoint. Take advantage of that if you need, then just walk down the street. Very shortly, you'll see a large set of multiple stone stairways on your left. Clear the area and loot the treasure chest across from the stairs, then head up these stairs:

At the top of the stairs, you'll see a hole in the wall of a burning building. Ignore your sense of self-preservation and indulge your gamer's desire for loot and head into the burning building through this broken wall:

Walk down the stairs just inside the hole in the wall. This leads to a short passage leading to the basement shop of a clockmaker. As your character notes, there's a lot of clocks in here. At the entrance to the clockmaker's shop, head through the door on your right and climb the stairs to find a Tome of Knowledge:

Head back to the shop and read the note on the crate, which tells you that "the flywheel" is in "the house clock," and to "Look to the tower" to figure out how to open it. The house clock is the large, cuckoo clock above the clockmaker's workbench:

To solve this, you'll need to head to Hewdas Clock and note the time on its clocks. Then, return here and set the house clock to match the time on Hewdas Clock. Here's the solution in game:

When you open the house clock, the Clockwork Pinion quest item drops onto the workbench. Pick it up, loot the treasure chest next to the workbench, and return to Hewdas Clock to reap the real reward.