I think it is a good bet that he was born in Indiana - not only is this indicated in his 1850 and 1860 census records, but his daughter Melvina in the 1900 census, his son James Jackson in the 1880 census, and his son Elijah Lee in the 1880 census also all said he had been born in Indiana.
There is indeed a Moses Lee in Lawrence County, IN, in the 1820 census, and another one in Vermillion County, IN, in the 1830 census. The ages and numbers of children suggest these two may be the same, although the two counties are in different parts of the state. Both censuses also include a boy in the family of the right age to be Elijah.
The next step would probably be to check the probate records in Vermillion County, IN, to see whether there is a probate record for Moses that would indicate he had a son named Elijah (a bonus would be if it were to list a son Elijah of Arkansas). Unfortunately, while the LDS has filmed the probate records, they can be viewed only in a Family History Center or Affiliate Library.