Final answer:
The Lutheran doctrine stating that salvation is achieved through faith alone, not by good works, is called Sola Fide or Faith Alone. The correct option is A.
Step-by-step explanation:
The Lutheran doctrine that teaches Christians cannot earn their way into Heaven and that salvation may only be achieved through belief and faith in God's promise to redeem mankind is called Sola Fide, or Faith Alone.
Martin Luther, after a profound spiritual crisis and the study of St. Paul's writings, notably 'The just shall live by faith' (Romans 1:17), concluded that only faith, not good works, could secure salvation. This was in direct contrast to the Roman Catholic Church's teaching at the time, which held that salvation was achieved through a combination of faith and good works.