Jasper Newton Acree was your great-great grandfather (not 3 greats). His son, James Elliott was your great-grandfather, and Grandpa Lorin was James son.
Jasper Newton Acree had a half-brother named James, and I suppose that may be why he named his own son (our great-grandfather) James. I believe you are correct that he was an orphan, but his father MAY have been named Lewis Acree. Jasper was married to Mary Haley Cravens, but I don't know if that was a first or subsequent marriage.