Proceed further into the basement. You'll locate a locked door here and you'll find out that the gunsmith is being held in cell number 9. Ask Elizabeth to break the lock (you don't need any lockpicks for this action) and enter the prison.
There's a room with items prepared for recycling on the other side of the door. Examine the crates located close to the furnace and you'll find a Vox cipher needed to complete a side mission in the Plaza of Zeal.
Go past the projection room to end up in a corridor with the cells. Locate a lockpick and Voxophone #41 near the entrance.
If you've spared Slate during an encounter in the Hall of Heroes, then you'll find him in cell number 6. Take a Hand cannon and some ammunition from the table.
Ask Elizabeth to open the door leading to cell number 8 (you must have 5 lockpicks). Pick up Gear #19 - Head found next to a dead prisoner.
You must now unlock cell number 9 and the good news is that you don't need to have any lockpicks. Descend the stairs to get to a dark interrogation room. Check the table next to the cell to find a lockpick hidden behind a crate.
Enter a new room and use a glowing switch on a wall to turn on the lights. This will allow you to find Chen Lin's body. The Lutece siblings will arrive here shortly and thanks to them Elizabeth will be able to open a tear to an alternate world in which the gunsmith is still alive. Make sure that you've collected all the items from this location, because after you've advanced to the next chapter some of them will disappear or others will be replaced by new things.