Pick the colour in the crafting menu, not at the research table. Green has no blueprint and no research cost of its own: it is a skin of the plain sky lantern. Select the lantern, switch to green if your account owns it, and craft. The plain lantern is itself limited to players who own it on Steam, so both have to be yours.
Nothing else moves. The cloth is the same, the fuel is the same, and once lit a green lantern flies like any other. If your group signals neighbours by colour, green is an easy one to agree on. If not, the choice is pure looks, and without the skin you craft the same lantern in its default colour.
Questions
Sky Lantern - Green ×10: how many resources?
Cloth ×113, Animal Fat ×39.
Which workbench does Sky Lantern - Green need?
None: it is crafted by hand.
How long does Sky Lantern - Green take to craft?
12 s for one, every step included.
How much scrap does researching Sky Lantern - Green take?