Hm. Would this wreck any key plot beats? The Ob ends up using the lantern in adventure 7 to placate some folks, and in adventures 8 and 9 to sneak forces in from the Bleak Gate, and in adventure 13 to stabilize the colossus as he tries to work on the Axis Seal. So there actually
aren't that many opportunities where this would be useful. If the party does want to pursue this, you might come up with some other scenes where the Ob tries to use a lantern offensively.
I'd say the idea is doable, but that you can't just use 'material plane' oil to negate other planar effects. You'd have to have a suite of different oils that have energies of different planes, and you'd have to figure out what type of energy the other lantern is using, and fill your lantern with the 'antidote' of sorts.
Just for the sake of verisimilitude, I think it should be hard for the PCs to do this, because Luc Jierre spent years inventing the lantern. It should be more involved than just 'spend some gold and make a single skill check' to figure out how to do the same yourself.
If they wanted to figure out how the lantern works from a scientific sense, I would require a few months of trial and error. Like, require a week of work, and then call for a DC 25 Knowledge (arcana) check, and a DC 25 Knowledge (planes) check to figure out each one of the prerequisites to craft the item. And the prerequisites would be: Craft Wondrous Item, caster level 9th (those two are obvious and don't require checks), then the ability to cast Plane Shift, and eight other spells, one for each of the eight elements the lantern uses.
So at least one spell with each of the following descriptors - air, earth, fire, teleportation (for space), and water - plus something like Inflict Light Wounds (for death), and Slow or Haste (for time).
If they have a copy of the lantern to study, give them a +10 bonus to their Knowledge (arcana) checks, and if one of the PCs is a Skyseer they'd get +10 to their Knowledge (planes) checks. Maybe have some small mishaps in the lab if they fail a check by 5 or more. Work it in as a montage between adventures.
Once they figure out how the lantern works, they can build a lantern of their own if they need one (the RHC would foot the bill), and can try to make new oils. Getting an oil requires either them being able to travel to another plane, so they might be able to get Dreaming and Bleak Gate (life and death energy) and also thanks to ziggurats they've encountered get Mavisha and Apet (water and space). Clever ideas can find other planar energies, like how the Obscurati mine meteorites on a glacier in adventure 7.
Once they have oils, though, if they see there's another Wayfarer Lantern active, they could either use
detect magic and make a Spellcraft check (DC 20), or make a Knowledge (planes) (DC 25) check to figure out what type of energy is being used. Then as a full-round action they could load their own lantern with the right types of oils to be the 'antidote,' and then wherever the areas overlapped, the effect would be negated. (But in the areas that don't overlap, the PCs' lantern might have some weird effect of its own.)
Okay, that's possibly way too complicated, but temporarily making other planes coterminous should be hard. Until you're at least 15th level.
