Is there a Buddhist equivalent to Lutheran doctrine of Justification? I read on the internet Martin Luther said:

No sin can separate us from Him (Christ), even if we were to kill or commit
adultery thousands of times each day.
the Law shows us our inability to contribute anything to
justification.

Is there a Buddhist equivalent to Lutheranism (Christian Protestantism), namely, a Buddhist doctrine of salvation by faith alone?
Would this qualify as true dharma?
Yes and no.
No: The term “sin” does not have any special connotation in Buddhism, as it has in major theistic religions like Christianity, Judaism, or Islam. In all these religions, the general belief is that sins are individual actions which are contrary to the will of God or to the will of the Supreme Being. The karmic principle is based on action and consequence.
In Buddhist thinking the whole universe, men as well as gods, are subject to a reign of law. Every action, good or bad, has an inevitable and automatic effect in a long chain of causes, an effect which is independent of the will of any deity. Even though this may leave no room for the concept of 'sin' in the sense of an act of defiance against the authority of a personal god, Buddhists speak of 'sin' when referring to transgressions against the universal moral code. In addition, Buddhism has no concept of &quot;original sin&quot; like Christianity.
Yes: If you consider all of the above:

deities are subject to the same karmic principles as all other living beings
there is no comparable concept of sin, just action and consequence

then the principle of Pratītyasamutpāda comes very close. Commonly translated as dependent origination, or dependent arising, it is a key doctrine of Buddhist philosophy, which states that all dharmas arise in dependence upon other dharmas, i.e. that everything is interconnected and nothing can truly be separate.