Add the double sided flag on the material. Assuming you have something like:
material = new THREE.MeshLambertMaterial ({ color: 0xFF00FF });
add:
material.side = THREE.DoubleSide;
or when you create the material do:
material = new THREE.MeshLambertMaterial ({ color: 0xFF00FF, side: THREE.DoubleSide });
EDIT: For the OBJMTL loader that returns an Object3D we would then need to traverse the object to set the appropriate flag:
if (object instanceof THREE.Object3D)
{
object.traverse (function (mesh)
{
if (! (mesh instanceof THREE.Mesh)) return;
mesh.material.side = THREE.DoubleSide;
});
}