Joseph Smith emended the text here by adding “my father” to Lehi’s name (although in 𝓟 he supralinearly inserted the phrase in the wrong place—namely, before the subordinate conjunction after). It is possible that the original text had “my father” (the original manuscript is not extant here) and that somehow this noun phrase was accidentally lost. As far as we can tell, Joseph Smith did not use 𝓞 to restore readings in his editing for the 1837 edition. (Such a use of 𝓞 is found in his early editing for the 1840 edition.) So the change here in 2 Nephi 4:12 appears to be due to Joseph’s expectation that Nephi would use “my father” when stating the name Lehi.
Earlier in the text, Nephi always uses “my father” whenever Lehi’s name is explicitly stated (nine times); there is also one occurrence where Nephi writes “our father Lehi” (in 2 Nephi 1:1). It should be noted that Lehi is used without “my father” in the prefaces to 1 Nephi and 2 Nephi, but these prefaces are basically written in third person, not first person. Similarly, Nephi consistently uses “my mother” when he explicitly states the name Sariah (three times, excluding the one occurrence in the 1 Nephi preface).
But there is one thing different here in 2 Nephi 4:12. In this verse, Nephi ends up announcing the death of his father, which may explain why Nephi refers to Lehi without the expected “my father” or “our father”. It may very well be that after a parent dies, family members can refer to them by name only, but while living they are always identified as one’s parent (thus “my father Lehi” or “my mother Sariah”). In other words, after one’s death this honorific addition may no longer be necessary. Such a difference may explain why Jacob, the brother of Nephi, does not add “my father” or “our father” at the start of the book of Jacob; by this time Lehi has been dead for some years:
Of course, Jacob can still directly refer to his relationship with his father (as in Jacob 2:34: “these commandments was given to our father Lehi”), but it was no longer necessary. The fact that Jacob 1:1 uses Lehi without “my father” or “our father” suggests that the original usage in 2 Nephi 4:12 may be intended.
Of course, the use of Lehi without “my father” in 2 Nephi 4:12 is technically premature since Lehi was still alive when he spoke to all his household. But in anticipation of announcing Lehi’s death later in the verse, Nephi may have been led to drop the identification of Lehi as his father. David Calabro also points out (personal communication) that the question of whether Lehi is living is determined within the narrative itself, not when it was actually written by Nephi. Later in 2 Nephi 5:27–34, Nephi explains that the small plates of Nephi were written after Lehi’s death. Even so, within the narrative itself, Lehi is alive until 2 Nephi 4:12, and thus the use of the phrase “my father Lehi” is necessary prior to that point.
Summary: Restore in 2 Nephi 4:12 the use of Lehi without “my father”; after the death of Lehi, family members could apparently refer to him simply by name (as in Jacob 1:1).