The Lord's Private Chamber can be accessed immediately after defeating The Duke's Dear Freja. To get there, follow the narrow tunnel leading out of the cave. The chamber connects to another larger room with a primal bonfire. The body of Vengarl can be found guarding the bonfire (not found in Scholar of the First Sin).
The Lord's Private Chamber is a small room with a table, several bookshelves and countless books. A hostile undead, Lord Tseldora, is also inside.