When you say that half the picture is missing, do you mean that the frame is cut off on the negative?
Otherwise, I am thinking that you may have loaded it wrong, or the camera wasn't advancing properly, or binding, or something. I'm not familiar with the Lomo cameras specifically, but the principle of advancing film across a plane is pretty standard for roll film. If the film was not properly loaded on the take-up side, then you could have all kinds of problems of double/over exposure, half-frames, unexposed bits, etc.
A word of caution... you would also want to be careful how you hold it as the winder is on top of the camera. If your finger is pressing on this bit while you wind it, it will not allow the film to advance easily and might give you problems as well. If this winder spins when you are advancing the film, it should be OK (although the first few frames might not spin as it is still pulling the slack out of the film spool/canister).
Good luck, and don't let a bad experience deter you from shooting more film