To reach the 2F of the Lecture Building you’ll need to head to the Advent Plaza, where you defeated The One Reborn, and check the mummy on the nearby building to teleport to the Lecture Building.
Enter the circular room across from the lamp for the Sedatives x6 and then cross back to the lamp side of the building to head down the hall, dealing with the multiple Scholars. The large room on your left overlooks the Lecture Theatre, where all the Scholars are seated, but there is only a Lore Note in the rooms on this side.
Continue to the other side of the building, where you’ll encounter a Church Giant with flaming fists, and then climb down the ladder into the room with Patches the Spider for 2 Insight .
If you let Patches push you off the ledge in the Nightmare Frontier you can speak to Patches multiple times to gain the Beg for Life and Anti-Clockwise Metamorphosis Rune, provided you select "Not at All", and he will now be available in the Chalice Dungeons as a merchant.
Return upstairs along the balcony, killing the Scholars, to grab the Blood Stone Chunk at the end and then backtrack toward the ladder. Open the door to the nearby Lecture Hall and cross the balcony to the other side, where you can open a chest with the Communion Rune.
You can now leave the 2F through the glowing door on this side of the building to enter the Nightmare of Mensis.
Note: The Nightmare of Mensis lamp is actually outside the cave, up a hill with a Loran Silverbeast and Wandering Nightmare, and past a Frenzied Coldblood (9) , where the light from the window will cause Frenzy to slowly build up.