One wonders here at the beginning of verse 29 whether the text should read “and this was also a cause of much sorrow among the Lamanites”, especially since the same dissenters are causing sorrow for both the righteous Nephites and Lamanites.
In clauses that state “X (not) to be a/the cause of something”, the X can be a subject pronoun, a noun phrase, a relative pronoun, an interrogative pronoun, or (in one other case besides 3 Nephi 1:29) the existential there. Here I list the various possibilities for X (including representative examples) and the number of times that form of the subject occurs in the text:
subject pronoun
noun phrase
relative pronoun
interrogative pronoun
existential there
Here the negative existential is equivalent to “that there should not be any cause for unbelief ”.
Since here in 3 Nephi 1:29 the printer’s manuscript and the 1830 edition agree (both have there in 3 Nephi 1:29), the original manuscript undoubtedly read there. Although the text may be referring to the same cause in both verses 28 and 29, it is also possible to see a distinction: the Nephites were sorrowful because so many Nephites were dissenting over to the Gaddianton robbers, while the Lamanites were sorrowful because so many of their own children were joining the Gaddianton robbers. So there will work in 3 Nephi 1:29 and will be maintained in the critical text.
Another aspect that makes it doubtful that there is an error for this here in 3 Nephi 1:29 is that elsewhere in the transmission of the text there are no examples where there and this have ever been mixed up. Another possible mix-up, pointed out by David Calabro (personal communication) is that there could be an error for they; that is, the original text may have read “and they was also a cause of much sorrow among the Lamanites”. The nonstandard they was would not be a reason for rejecting this proposed emendation since such usage is found in the original text (see the discussion under 1 Nephi 4:4, where the earliest text read “they was yet wroth”). Here in 3 Nephi 1:29, Oliver Cowdery could have misheard an original they, referring to the Gaddianton robbers, as there. And there is evidence that Oliver sometimes wrote there instead of they in his manuscript work, if only momentarily:
It should be noted that in this proposed emendation for 3 Nephi 1:29 the passage ends up with three different referents for the pronoun they (first the Gaddianton robbers, then the righteous Lamanites, and finally the Lamanite children):
Yet as discussed above, there (the reading in both 𝓟 and the 1830 edition) works well enough in this passage, so there is no strong reason to emend there to they.
Summary: Accept the unusual but acceptable use of there in 3 Nephi 1:29: “and there was also a cause of much sorrow among the Lamanites”; the there here is probably not an error for this or they.