Strict prescriptivists of English grammar attempt to distinguish between intransitive and transitive forms of the verbs lie and lay:
intransitive lie, lay, have lain
transitive lay, laid, have laid
Probably very few English speakers consistently make this distinction, despite all the attempts of prescriptivists to enforce this purported rule. (Consider, for instance, the universally spoken but supposedly incorrect “Let’s go lay out this afternoon”, referring to getting a suntan.) If one wants to follow this artificial distinction, then laid should be replaced by lain here in 2 Nephi 9:7 (as in fact was done in the 1953 RLDS edition).
There are two examples in the history of the text where the infinitive form lay has been edited to lie. Joseph Smith was responsible for both these instances of editing:
In these two cases, as with 2 Nephi 9:7, the original text used the verb lay intransitively. For all three cases, the critical text will retain the original usage. For further discussion of this issue, see lay, lie in Merriam-Webster’s Dictionary of English Usage. Also see lay as well as past participle in volume 3 of the critical text.
Summary: Maintain the normal but supposedly nonstandard laid in 2 Nephi 9:7 (“this flesh must have laid down to rot”); similarly, intransitive uses of the verb lay will be restored in Omni 1:30 and Alma 24:23.