The Lord's Private chamber can be accessed after defeating the second boss of Brightstone Cove Tseldora. Head into the tunnel from the boss area and shortly afterwards you will come to a short hallway with the hollow duke staring at a table in a small room ahead with his back to you. Run up behind for a quick back-stab or just used ranged attacks to bring him down. Upon death, he will drop a Fragrant Branch of Yore, Dark Quartz Ring +1 and the Brightstone Key. The key can be used to access a room in the second half of the Brightstone Cove Tseldora area. Just look for the "Brightstone Key Room" heading in the Brightstone Cove Tseldora section. From the table the duke was standing in front of, turn right to see a set of stairs heading downwards. Down the stairs is Vengarl's body (remember the head we talked to in Shaded Woods? His body guards the primal bonfire). Defeat the body to obtain the rest of his armour set and return to Vengarl later and he will sell equipment to you. When you are done with this small area, light the primal bonfire and return to Majula.