Looks like Lawson was older then Fannie, was divorced before he married Fannie, and died between 1897, when youngest James Walter was born, and 1900 census when Fannie shows up as a widow.
1900 census Kaufman Co, TX:
Green, John W., h, b Sep 1829, 70, m 40 yrs, b GA, GA, GA
" Mary E., w, b Sep 1835, 64, m 40 yrs, 2 ch, 2 lvg, b FL, GA, FL
Sneed, Francis, d, b Sep 1862, 37, wid, b FL
Green, John J., s, b Mch 1865, 35, sgl, b FL
Derrington, L.D.S., gr dau, b Sep 1885, 14, b TX, MO, FL
" Eva L., gr dau, b Nov 1888, 11, b TX, MO, FL
Sneed, Edgar G., gr son, b Jun 1889, 10, b TX, FL, FL
" John J., gr son, b Aug 1891, 8, b TX
" Roy H., gr son, b Jul 1894, 5, b TX
" James W., gr son, b Apr 1897, 3, b TX
Fannie is only 37 on the 1900 census, I'm betting she remarried.Roy is 14 and a boarder in someone else's household in 1910, sounds like he moved out and away from a stepfather????I would look for marriage records, see if you can find who she married the second time.
Happy Hunting (^_^)