I feel certain this is the same Jesse Crocker who, at the time of the 1860 US Census, was living with his older brother Thomas' family, in Buck & Breck, Precinct No. 3, Dallas Co., Texas. Living adjacent to the Crocker family was the household of one Jas W Lane. The listing includes one Octavia J Lane, female, age 8, born in Texas. Her out-of-order listing would appear to indicate that she was not the child of Jas W Lane, but rather a relative or possibly an orphan.
In 1870, Jesse, his wife and young daughter were in Industry, Austin Co., TX, living next to his nephew John and family. Also a member of his household is someone named "Octava Lane," female, now aged 18, born in Texas. I can conceive of no possibility in which these could be two completely different groups of people.