Wire termination under cabinet
Led lighting typically requires a transformer or power supply.  The power supply is plugged in or hardwired somewhere that is hidden like under the sink or on top of the cabinets.  Low voltage wire 18/2 is then typically run from this location to each location that requires led lighting.
You could use your armored cable to carry low voltage if you know where the cable ends and can disconnect it from the actual junction box.  At that junction box you could then hookup the power supply and splice the low voltage output onto the armored cable to supply the led fixture under the cabinet.
I don't think there are any gfci requirements for low voltage lighting in proximity of a sink.