Are you looking for a campfire type? A lit furnace is an item smelting / cooking. It only stays lit while item(s) are smelting. A campfire stays lit or unlit continuous. A lit furnace is 1 item to cook / smelt in top and 1 combustible in bottom (coal, blaze rod, lava bucket etc)
Nope. The schematic shows an actual lit furnace. Not a campfire. I could make due with a regular furnace, but I'd like to stay true to the build's creator. Edit. The Lit Furnace is no longer available as an item (at least as multiplayer is concerned). See Technical Blocks/Lit Furnace. I'll just have to make due with a normal furnace.
There isn't any vanilla way to place a lit furnace. You are just going to have to place a unlit furnace or have something else to replace it