The 1920 LDS edition intentionally deleted the he at the beginning of the final conjoined predicate, probably because there is no subject pronoun for the two preceding conjoined predicates (“and went forth and bowed himself before the Lord”). The change is marked in the 1920 committee copy. Another possible reason for the 1920 emendation was to prevent the reader from misinterpreting the he as referring to the preceding the Lord—as if the Lord himself kissed Nephi’s feet! Yet it seems very doubtful that any normal reader would ever misread the text in this way.
The original extra he separates Nephi’s actions into two parts (first, getting up, going forward, and bowing down before the Lord, and then kissing his feet). There are a few other examples in the current text where the use of and he did introduces a division, as in the following example:
Clearly, there is nothing inherently wrong with the pronoun he in 3 Nephi 11:19, nor is there really much chance of misinterpreting the pronoun he as referring to the Lord. One alternative emendation that the 1830 typesetter could have chosen in order to avoid this minor difficulty would have been to replace the he with Nephi: “and Nephi did kiss his feet”.
Summary: Restore the pronoun he in 3 Nephi 11:19 (“and he did kiss his feet”); the original use of the full clause appears to separate a group of actions (all dealing with approaching the Lord) from the last one (kissing his feet).