The 1830 edition has the plural words, the printer’s manuscript the singular word. The probable reading of the original manuscript was the plural words. Note, for instance, the use of the plural words later on in this verse:
Similarly, in verse 25 we have “and they did fear the words which had been spoken by Lachoneus”. There is one other instance in the text where words is conjoined with prophecies:
As noted under 1 Nephi 16:24, the Book of Mormon text typically uses the plural words to refer to the word(s) of a person.
Nearby, in 3 Nephi 1:16, we have a case where 𝓟 reads words and the 1830 edition reads word. We have the opposite situation here in 3 Nephi 3:16, with 𝓟 having word and the 1830 edition having words. When we consider mix-ups in the early transmission of the text, we can find considerable evidence of Oliver Cowdery writing word in place of words. There are 12 instances in the manuscripts where he initially wrote the singular word instead of the correct plural (for some examples, see under Alma 42:31). And there is one clear case where he did not catch his error as he copied from 𝓞 into 𝓟:
He apparently made the same error in 𝓟 for Alma 42:31, although the evidence there is more complicated (see the discussion under that passage). In contrast, we have three instances where the 1830 typesetter accidentally replaced the singular word with the plural words:
Since the error could have been in either direction here in 3 Nephi 3:16, we will rely on internal evidence (that is, usage elsewhere in the text) in order to determine the more appropriate reading. And that evidence supports the plural words, the 1830 reading.
Summary: Accept in 3 Nephi 3:16 the 1830 reading in the plural (“the words and prophecies of Lachoneus”) since this reading is more consistent with usage elsewhere in the text than is the reading in 𝓟 (“the word and prophecies of Lachoneus”).