Yes balanced is possible, just need them to be designed appropriately. We will provide more information on this later.
LCD-1 cable is comprised of two shielded stereo cables that are connected in parallel to a single 3.5mm TRS connector (going to the amp). Each of the shielded stereo cables terminate as 3.5mm TRS connector going into each of the ear cups. There are sufficient wires available to easily reterminate to whatever balanced cable termination you desire or build your own.
Each earcup is connected to respective left or right contact on female connector inside earcup. Return wire in both cases is shield from the cable that is connected to respective earcup. Obviously, care needs to be taken not to short shields from both cables on the balanced connector because that defeats the purpose of balanced connection and in most cases can create problems with amplifier. Right now the cables are not marked left or right because they are L/R agnostic but if using a balanced configuration then Left/right marking can be easily made with heat shrink of desired color.