Last Servicemember Standing Medal Act This bill establishes the Last Servicemember Standing medal for certain members of the Armed Forces. A person eligible for the medal is any servicemember who served on active duty; was deployed during war or an overseas contingency operation; as a result of a combat instance during such war or operation, was the last surviving member of a unit; demonstrated extraordinary heroism during such combat; and whose character is recommended for recognition by their commanding officer and at least two peers. The medal may be issued to the next-of-kin if the recipient is deceased.