First, you will need to have progressed far enough to get the generator working again, and got Lily down to Dougal. I have guides up for both of these achievements.
1: Grab the footstool from the house, and make your way to the Shed.
2: Once inside, attempt to grab the item from the top. The shelf will break.
3: Next you will need to use the footstool on the broken shelf, but will fall, and knock the item to the floor.
4: Use the mask with Dougal, then approach Lily and use the box with her. She will do a strange dance, with each pose resembling a pose icon on the box under each of the 4 finger slots. Simple puzzle. But you must get it right first time. Otherwise you will need to start a new game.
To get this done right, I'll try and explain as best I can.
1st pose: Both arms up in the air, standing up.
2nd pose: Both arms up in the air, crouching.
3rd pose: One arm in the air.
4th pose: Handstand.
Hope this helps.