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Is my interpretation of these rules correct?
Throwing a lantern to attempt to hit a specific spot on the ground 50ft away.
So total of -12 to attack roll against a target of 5. If it's a miss, roll 1d8 to determine direction and it hits 5ft for every range increment in that direction.
All correct except for the range penalties: you take the penalty when you meet a range increment, not when you exceed it.
Range Increment
Any attack at less than this distance is not penalized for range.
(Weapons > Range Increment, emphasis mine)
So 50 feet with a 10-foot increment is five increments, for –10.
Yes, this means weapons with 10-foot range increments are pretty much always taking range penalties. And yes, this is really counter-intuitive and almost everyone initially assumes it works the way you thought, and I’m sure many play that way without incident.
The Monster Manual on Swarm on Combat says, "A lit lantern can be used as a thrown weapon, dealing 1d4 points of fire damage to all creatures in squares adjacent to where it breaks" (237). (I suspect this use of a lantern assumes that the goal is to throw the lit lantern so it breaks, deliberately to immolate one's foes with its contents. Seriously, an adventurer's lantern should withstand casual abuse absent explosive consequences… unless, of course, the DM's plot involves a sinister cabal of shoddy lantern-makers or whatever.)
Unfortunately, the text omits what kind of thrown weapon the lit lantern counts as—improvised, exotic, martial, simple, or splash—, but given the earlier description of the torch ("A lit torch swung as an improvised weapon deals 1d3 points of fire damage per hit"), this reader assumes, because the author seems aware of improvised weapons, that to throw a lantern requires no particular proficiency, much like it doesn't take proficiency to throw a splash weapon. Further, a "splash weapon is a ranged weapon that breaks on impact, splashing or scattering its contents over its target and nearby creatures or objects," says the Player's Handbook (158), and that's pretty much exactly what happens in the description of hurling a lit lantern, above.
Thus, as per the question's example, this DM would rule that a creature that throws a lit lantern at a grid intersection that's 50 ft. away makes an attack roll against AC 5 and suffers a −10 penalty on that attack roll due to range. Success means that the grid intersection is hit and that creatures in squares adjacent to that grid intersection are dealt 1d4 points of fire damage. Failure means that the DM consults the diagram Missing with a Thrown Weapon (ibid.) and rolls 1d8 with the lit lantern instead breaking 5 intersections in the indicated direction from intended target intersection.
Note: So far as I'm aware, the swarm entry of the Monster Manual is the only place the game mentions weaponizing a typical lantern.
