The Book of Mormon text has examples of both “faith on someone” and “faith in someone”; in fact, in every case that someone is the Lord. Yet the text is almost totally systematic in its choice of on or in in terms of the specific words used to refer to the Lord:
faith in X (36 times)
Christ 14 times
him 9 times
me 5 times
God 4 times
the Holy One of Israel 1 time
Jesus Christ 1 time
my Well Beloved 1 time
the Lamb of God 1 time
faith on X (13 times)
the Lord Jesus Christ 6 times
the Lord 5 times
the Son of God 1 time
the Lamb of God 1 time
The only case where there is actual variation is with “the Lamb of God”, with one instance of “faith in the Lamb of God” (1 Nephi 12:10) and one of “faith on the Lamb of God” (Alma 7:14). But for the specific phrase the Lord, the text strongly supports on, not in (5 to 0); thus the original reading here in Helaman 15:7 is completely appropriate.
There is more choice when comparing the phrases “faith in something” and “faith on something”. For discussion of variation in the preposition for those cases of “faith in/on his name”, see under Moroni 7:38 (where the original text read “faith in his name” but the 1874 RLDS edition changed the preposition to on).
Summary: Maintain in Helaman 15:7 the original use of on in the phrase “faith on the Lord”; elsewhere the text systematically supports the preposition on, not in, for the specific phrase the Lord.