You must have Lara actually read the inscription, by pressing Interact, in order to unlock the next clue in the puzzle.
NOTE: The visible words on the plaque say something completely different: "This Cloister is Erected/to the Glory of God and/in Loving Memory of/J a[?] E S Loyes/1853-1912/Daughters of the/American Revolution." The same words appear on other plaques in the manor. I'm not sure if this is an Easter egg with some significance or possibly a texture based on a real-life memorial somewhere, but it doesn't seem relevant to the game. Thanks to Iaian for pointing this out.
The passage continues to another tongue switch, which opens a concealed door leading into the BEDROOM. Open it if you like. Then return to the LIBRARY through the secret passage.