Once the lantern has lamp oil, a tinderbox is used to light it.
Bullseye lanterns can also be stolen from chests in Dorgesh-Kaan, which require either 52 or 78 thieving (either one yields them very often). They can also be stolen from cave goblins. Some of these methods will instead provide a bullseye lantern (empty) and still require the use of lamp oil to complete them, however.
This lantern can be used for one of the medium Falador Tasks: Light a Bullseye lantern in the Chemist's house.