The lantern I bought had a double floor. The construction is made of sheet metal, so it's easy enough to drill through. I used a Dremel to smoothen the edges of the holes. Be aware that sharp edges can cut through the wire over time, and this can result in electric current running through the lantern case and create the risk of an electric shock to the user.
- add extra tube around the wire
- use insulated wires as shown in picture, don't confuse with speaker wire that has only one layer of insulation and should never be used to carry mains voltages
As you see in the picture, I didn't drill the holes in the most convenient place. At the bottom of the lantern there were already some holes, and I started using one of those to drill through the floor.
On hindsight, drilling in the corner between two glass panels would have been better.