how about glowing mushroom? pretty common especially in falmer populated areas. alchemize or cook a number of them (5? 10?) for fuel that wouldn't last as long as long as the less common fat-based fuels. Also, if alchemized, the glowing mushroom fuel could be recharged by a spell.
I know it adds complexity to the mod, but it makes sense and is lore friendly. The problem would be refueling the lantern on the fly when you're in the middle of a dungeon.
I'll also say that the lantern on the back of the hip doesn't really gel... i mean realistically, you wouldn't be able to see in front of you. along the lines of the pole on the back, there is a fishing pole mesh in the game. you could attach BOTH the fishing poll and the lantern to the same slot, then offset the lantern to appear ta the top end of the pole. Of course it wouldn't have any physics and bounce around, but still.