Lowing the climber with a Petzl GriGri, the break strand of the rope jumped out of my hand. I believe the force was generated by a twist in the flaked rope. Likely due to not having a firm enough grip of the rope. This lead to the rope running freely through the GriGri and the climber almost free falling.
As soon as I realised, I let go the cam's handle in attempt to stop the fall and reached for the dead rope which was couple feet in front of me now. Luckily the cam engaged, catching the climber and I regained control of the deadrope.
I don't believe the climber experienced anything other than a metre or two of quick lowering as neither they or a third person with us were alarmed.