You need: Mario, Red blocks unlocked
1) Go through the brown doors next to the lobby stairs.
2) Go to the far door and enter the courtyard (it should have a bunch of Boos)
3)Hit the Big Boo to enter the world where Luigi is.
4)Complete the first mission and the stairs should rise (if not keeping playing through the missions). Go to the 2nd floor and enter the far right door.
5) Hit the red block and float up to the platform above. Enter the door and the Luigi painting is right next to it!