The Collaborative International Dictionary of English v.0.48:
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. [1913 Webster]WordNet (r) 3.0 (2006):
lineally adv 1: by an unbroken line of descent; "she is related lineally to the Royal Family"