As discussed under Alma 22:22, there are several instances in the original text of the Book of Mormon (as well as in the King James Bible) of lest that. For this instance in Alma 36:11, the word perhaps intervenes, which may have had something to do with Joseph Smith’s decision to remove the that from “lest perhaps that” in his editing for the 1837 edition. For the two examples of lest that (listed under Alma 22:22), Joseph never removed the that in his editing.
There is one more example of lest perhaps in the text. In this case, there is no that (based on the reading in 𝓟 and the spacing between extant fragments of 𝓞):
So Joseph Smith’s removal of the that in Alma 36:11 is consistent with this one other example of lest perhaps in the Book of Mormon text. It is also consistent with the only occurrence of lest perhaps in the King James Bible:
In any event, the critical text will restore the original that in “lest perhaps that” in Alma 36:11 since it is clearly intended.
Summary: Restore the original that in Alma 36:11 (“lest perhaps that I should be destroyed”).