How to build loss-free inverter?
You just have to buy a NC-switch. There are a lot of these devices.

If you don't want to change the type of the switch (I'm assuming you have some sort of NO-switch), you can flip the switch around, add a spring which keeps the NO-switch in the closed position and add some sort of a lever which acts against the spring. The lever then can be moved by closing the box. 

Edit

After having understood OP's self made switch's principle, I feel urged to deliver another self made NC-solution. 

Fix a clothes-peg inside the box with its mouth facing towards the box' cover. Do it by e.g. glueing or screwing one lever to the wall of the box. Put tin foil onto the other lever and contact it with another tin-foil wrapped plastic or wood piece glued to the bottom of the box. Then apply a nail to the box cover so that it opposes the clothes-peg's mouth. When the cover is put in place the nail should pry the mouth of the peg open lifting the moving lever away from the foil wrapped piece. That's your NC-switch.