LA Noire Launcher DirectX not found problem (Windows XP)
Solution 1:
Most likely, Steam is trying to launch the DX11 executable of the game instead of the DX9 version. Try opening the install directory of the game(located in your "steamapps" folder), check if there's a DX9 version of the executable and try running that directly.
EDIT: You can also try running lanoire.exe directly instead of the Launcher program