As explained under Mosiah 26:27, the expected word order in the Book of Mormon is “then will I”, not “then I will”. But in a couple of cases, the inverted word order has been replaced by the noninverted order, as here in the 1852 LDS edition for 3 Nephi 16:11. The 1920 LDS edition restored the correct order to the LDS text (most likely by reference to one of the earlier editions). The change was marked in the 1920 committee copy.
Summary: Retain in 3 Nephi 16:11 the original inverted order, with the auxiliary verb will preceding the subject (“and then will I remember my covenant”); usage elsewhere in the original text consistently supports the inverted word order after then.