In modern English we do not expect that after the subordinate conjunction lest. In this passage, the 1953 RLDS edition removed the that, perhaps unintentionally. Elsewhere in the Book of Mormon text, we have 72 occurrences of lest without any that before the following finite clause, as in 1 Nephi 8:36: “yea he feared lest they should be cast off from the presence of the Lord”. But there are two other original cases in the text where lest is followed by that:
The first of these was grammatically emended by Joseph Smith in his editing for the 1837 edition, but the last one has never been altered. The fact that the 1953 RLDS edition maintained the that in this last example suggests that its omission in Alma 22:22 was accidental. Of course, the natural tendency would be for modern English speakers to remove the that after subordinate conjunctions like lest. The original text generally permitted that after subordinate conjunctions (such as after and because). For further discussion of such archaic usage in the original text, see under subordinate conjunctions in volume 3.
There are numerous citations of lest that (with that precise spelling) on the online Oxford English Dictionary, with dates from 1385 to 1671; of course, that phraseology is now obsolete. For some examples of lest that from the printed OED (all with alternative spellings of lest that), see the section lest that under the conjunction lest. The King James Bible normally has just lest, but there are two examples of lest that:
The critical text will accept all the original instances of lest that in the Book of Mormon text.
Summary: Maintain in Alma 22:22 the original that after the subordinate conjunction lest; similar usage can be found elsewhere in the original (and current) text of the Book of Mormon as well as in the King James Bible.