Watch as Lakshmi meets Sir Lucan. After the proper introductions, another big squad of Company guards attacks from across the open lobby (38).
This is a tough fight—use cover well and unleash your Blacksight on the swarm. Grab the ammo crate (39) sitting on a low cabinet in the left corner when you run low. When you clear the room, Lucan rushes ahead and says, “Let’s move! The archives room is this way.”
Climb the curving staircase (40) that leads up to the west balcony. Before you move onto the courtyard balcony as Lucan directs, find the “Ramayana, First Verse” phonograph cylinder (41) at the far end of the long table in the dining room. Then get ready for some more wild combat.
When you approach the balcony, all hell starts buzzing down in the courtyard. You must eliminate all attacking guards before you can move on. You have a nice weapon option here—a cache that includes a TS-17 Detonator plus an ammo crate sits on the balcony benches (42). Start launching explosive detonator charges at the guards below. Remember that you must detonate them yourself. Just tap your Alt-Fire button 
to detonate the last charge you fired, or hold it in to detonate all charges fired.
When the courtyard is cleared, swap the Detonator for the Falchion again and help Lucan bash through the next set of doors (43) into the archives anteroom.