A new member is joining my party for Grim World. I wanted to give him a class he would find satisfying to play. He really enjoyed the concept of The Lantern Class, however I have no experience with Inverse World. Are classes from Inverse World compatible with Grim World? Should it be significantly modified? Do these two differ so much they shouldn't be played together?
If you have the Inverse World book, pages 104 through 109 are discussions of how and whether to use the Inverse World playbooks in games not set in Inverse World, including discussions of particular moves and mechanics that may be problematic and how to replace them. It'll tell you on page 106, for example, that the mechanics and effects of the Lantern are pretty portable just about anywhere. The problem is that a sizable amount of its direct and incidental lore mention Sola, you know, the light at the heart of the world, whose love keeps us close and warm and whose wisdom pours down like the rain.
Whatever the Lantern's got in a Grim World, it's not Sola's light and it doesn't burn with Sola's power. You'll need to come up with your own story about how that little shard of light has so much potential. ...I mean, maybe it actually is Sola's light, that broke through the roof of the world and went beyond, which would be really neat, but it's your call to make.
Also, the "how did you get your light" part of the playbook is the Inverse World equivalent of a race move, so they'll have to choose between that and the Grim World race move alternative. Inverse World playbooks in general don't have a "race" section, replacing it with a "background" section because they're a little more free-wheeling and crazy about how much variety there is among people. If the section on an Inverse World playbook isn't explicitly labeled "background" you can still tell it because it starts with "pick any race, then choose".
Also also, they'll need to come up with a death move, though if there isn't a Shaman that one looks pretty reasonable for a Lantern too.