Your Steam inventory decides this craft, not your scrap. The lantern shows up in the crafting menu only for players who have it as a Steam item, so there is no blueprint, no research and no bench to stand at. If it is missing from your menu, no amount of scrap will put it there.
For owners the price is almost all cloth. The fuel side is small but awkward: low grade fuel comes out in batches that one lantern never uses up, and the rest sits in your pockets. Queue them in fours and the fuel divides exactly.
The five colours are not five recipes. Green, orange, purple and red are skins of this lantern: you craft the plain one and pick the colour if you own it, so every coloured lantern shows this same bill. Next to a Chinese lantern, which also wants cloth and fuel, it is the cheaper craft, but it flies off and is gone, while the Chinese lantern stays on your wall.