A mining helmet is an item primarily dropped by Cave goblin miners. It is dropped unlit, but can be lit by players who have a Firemaking level of at least 65. It can also be purchased from Miltog's Lamps in the Dorgesh-Kaan market place. You can also get one from using the brooch on Mistag after completing The Lost Tribe quest.
Lighting this helmet in the Lumbridge castle cellar is a hard requirement for the Lumbridge & Draynor Diary.