Is the Board of Directors the fist line of defense under the COSO framework for risk management? It seems it is neither 1st, 2nd or 3rd LOD.

The Board is not part of the 3 lines of defense. The following is taken from an IIA publication "Leveraging COSO Across the Three Lines of Defense."

Senior management and the board of directors have integral roles in the Model. Senior management is accountable for the selection, development, and evaluation of the system of internal control with oversight by the board of directors. Although neither senior management nor the board of directors is considered to be part of one of the three lines, these parties collectively have responsibility for establishing an organization’s objectives, defining high-level strategies to achieve those objectives, and establishing governance structures to best manage risk.