Willow's lighter does not relight upon transition from interior to interior or interior to exterior. The instance of the lighterfire prefab upon equipping is not initialized with the inst.fire:AddTag("INTERIOR_LIMBO_IMMUNE") tag. Therefore, the lighterfire prefab does not survive interior limbo like a torch would. This change can be made in the scripts/prefab/lighter.lua file, adding the line to add the tag after line 25.
Steps to Reproduce
add inst.fire:AddTag("INTERIOR_LIMBO_IMMUNE") after line 25 in scripts/prefab/lighter.lua
This issue has not been confirmed by a developer yet.