robot-threejs | experiments in making a robot-based game using three.js | Graphics library

You're implementing THREE.LOD wrong.

1. The constructor does not take any parameters, so when you do this: new THREE.LOD(object);, it does nothing. You just have to use new THREE.LOD();
2. You're adding the same mesh to LOD 3 times, so you're not gonna see any difference. You need to create separate meshes with different geometries if you want to see any change in detail. Keep in mind that you have to generate these geometries yourself. Three.js doesn't automatically change the geometry for you. But you could use the SimplifyModifier for this.
3. Not sure why you're playing with matrix updates. There's no reason for this here.
4. You also need to call lod.update(camera) on your render loop if you want to see the change in detail.

I strongly recommend you read the documentation for LOD and read through the code in this example to better understand how it works.