I have thought about this before, knowing that I must be thinking of "mercy" in the wrong way, because I was primarily thinking of it from the perspective that it means "Lord, relent
Without having any knowledge of Greek, I just decided to look at English definitions, and I found this gem amidst the judicial uses which took primacy:
A blessing that is an act of divine favor.
I find this definition to be particularly useful, because it lacks any references to offense or leniency. Those can be associated with mercy, but for the Orthodox Christian they do not indicate its primary function.
So in reality, a better translation of the prayer than "Lord, relent" might be "Lord, give your blessing
Also, remember that "Lord, have mercy" is merely a translation of "Kyrie Eleison", one of the most ancient Christian prayers. It is in all Christian liturgies worldwide. It is the universal Christian cry.