1890 census is lost, so your not going to find him there,
you can look at the 1900 census to see if there is another LEE family living nearby that might be related.
Do you know if he had any brothers or sisters?
Or he might have named one of his sons after his father?
Good luck in your search
RED RIVER PJ WARD 3
FRANK LEE AGE 19 MAY 1881
parents bn Wn ?
AGE 28 ABT 1882 LA [parents bn LA
child: E. D. Lee age 0
pj ward 2 red river, la
Frank Lee age 37 abt 1883 LA
spouse Beulah age 30
J. D. Lee 9
pj ward 7 red river, la