Åke V. Ström posits that Joseph might have been influenced by Solomon Spaulding and/or Ethan Smith.
Åke V. Ström, "Red Indian Elements in Early Mormonism," Temenos: Nordic Journal for the Study of Religion 5 (1969): 130–131
The problem regarding the origin of this history of the invasions of America has engaged scientific research ever since the publication of BM in 1830. It is evident that Smith cannot have discovered all this himself. "He had neither the diligence nor the constancy to master reality, but his mind was open to all intellectual influences, from whatever province they might blow."
A possibility is that Smith had procured Ethan Smith's View of the Hebrews; or the Ten Tribes of Israel in America, (Vermont 1823, 2nd. ed. 1825), where the Indians are said to be Israelites and Indian legends similar to the story of the Flood arc quoted. E. D. Howe introduced another theory as early as 1834, that Smith had got the whole story from a lost manuscript by the clergyman Solomon Spaulding on the origin of the Indians. This theory was commonly accepted but was rejected by Riley and Meyer and was disposed of once and for all by Brodie, who proved that the only Spaulding manuscript that has existed was the one printed at Iowa in 1885, "an adventure story of some Romans sailing to Britain before the Christian era, who had been blown to America during a violent storm". Brodie manages to prove that the preserved affidavits about the existence of a second lost Spaulding manuscript are forgeries by an ex-Mormon called Philastus Hurlbut.
It is not wholly incredible that Joseph Smith may have heard about or even have heard the story read from Spaulding's manuscript about a parchment with a Latin text written on it which, it was maintained, was "found in a cave on the banks of Conneaut Creek" and afterwards translated into modern English. After the death of Spaulding the manuscript was kept by his wife in her husband's summer villa in Otsego county, N.Y. and was first printed at Lamoni, Iowa, in 1885, by the Reorganized Church.
To me it seems more probable that the non-Biblical material in BM and the whole story about the buried and discovered tablets, which are difficult to decipher and translate but which are seen to contain ancient tribal stories of the Americans, have quite a different origin. It is not a case of deliberate plagiarism or imitation, but a psychological process of the same kind as the Jewish and Christian reminiscences to be found in Muhammed's religious teaching. The thoughts of Lamoni and the conversation between Lamoni and Ammon (Alma 18:2-29, above p. 127) lead us to make a comparison between early Mormonism and the Lenni Lenape religion.