The monster throne immediately swapped the cowboy with Lynn, releasing the former and grabbing the latter, dragging her into the chair almost immediately and strapping her into it. The cowboy then took the chance to get out of the throne and picked up one of the phantom rifles that the throne had created.
He shot Lynn not once, but twice in quick succession that even Jin was not able to see until he saw the sparkles that came out from the bullet deflection that the anti bomb suit made. It was precisely because of the anti bomb suit that Lynn was not only able to survive the first wave of shots but also from the strangling of the throne.
The anti bomb suit did crack under the pressure of the stone hands but the subsequent barrages from the phantom rifles did a number on her anti bomb suit and it would break in the next few seconds if either Lynn or Jin did not do something about it.