Source : Webster's Revised Unabridged Dictionary (1913)

Lineally \Lin"e*al*ly\ (l[i^]n"[-e]*al*l[y^]), adv.
   In a lineal manner; as, the prince is lineally descended from
   the Conqueror.

Source : WordNet®

lineally
     adv : by an unbroken line of descent; "she is related lineally to
           the Royal Family"