Maybe u 've already done it but if not try to stick to the wall behind the chest and press the key to open, u may reach it through the wall
If it can't be, i remember a hidden switch for a bridge which may be either parallel to the one you have on picture 1 or come from the next room (the one on the bottom-left corner on your last picture). It has to be a bridge because you must get to it by means allowed by the game (i mean without tricks ) Look for the button and good luck.