Joseph initially came to Utah in 1850. (See the entry in Journal History, 21 December 1850, 2.) His surname is listed as "Luntsford" on the 1850 Utah census. Further research is needed to determine the name of the pioneer company he came to Utah with.
His father, step-mother, and siblings traveled to Utah in 1852. Although only Joseph's father, William, appears on the roster of the 1852 Outhouse Company as head of household, it also indicates that his traveling group consisted of nine adults and six children. As it is known that Joseph married in Salt Lake a few years later, it is assumed that he was among this group. Further research is needed to identify the other members of the traveling group.