The LORD and the Lord
This is a good question. In English the use of "Lord, lord" translates well. English readers can tell that this means men and women were coming to the Lord intensley beseeching or begging him, as lord, to receive something. However, in other languages the vocative forms translate differently.
"Lord, Lord" appears in the King James Version in: Matt. 7:21f 25:11; Lk. 6:46; 13:25. All of these forms are in the vocative case. Repeating the vocative also reads clearly in English. In English we repeat words of address to intensify the power of our request.
Additionally, in Hebrew, when words are repeated it can indicate the superlative form. The Hebrew might read "easy, easy" instead of "easiest" or, if the verb is meant, "do it as easily as you can."
That is the case with the uses of "peace, peace" in the following verses: Peace, Peace: 1 Chr. 12:18; Isa. 57:19; Jer. 6:14; 8:11.