The Collaborative International Dictionary of English v.0.48:

Lineal \Lin"e*al\ (l[i^]n"[-e]*al), a. [L. linealis belonging to
   a line, fr. linea line: cf. F. lin['e]al. See 3d Line.]
   1. Descending in a direct line from an ancestor; hereditary;
      derived from ancestors; -- opposed to collateral; as, a
      lineal descent or a lineal descendant.
      [1913 Webster]

            The prime and ancient right of lineal succession.
                                                  --Locke.
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   2. Inheriting by direct descent; having the right by direct
      descent to succeed (to).
      [1913 Webster]

            For only you are lineal to the throne. --Dryden.
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   3. Composed of lines; delineated; as, lineal designs.
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   4. In the direction of a line; of or pertaining to a line;
      measured on, or ascertained by, a line; linear; as, lineal
      magnitude.
      [1913 Webster]

   Lineal measure, the measure of length; -- usually written
      linear measure.
      [1913 Webster]

WordNet (r) 3.0 (2006):

lineal
    adj 1: in a straight unbroken line of descent from parent to
           child; "lineal ancestors"; "lineal heirs"; "a direct
           descendant of the king"; "direct heredity" [syn:
           lineal, direct] [ant: collateral, indirect]
    2: arranged in a line

Moby Thesaurus II by Grady Ward, 1.0:

69 Moby Thesaurus words for "lineal":
   after, arrowlike, attendant, cadet, catenary, clannish,
   consecutive, dead straight, diphyletic, direct, ensuing, ethnic,
   even, family, flat, following, genealogical, genetic, gentile,
   gentilic, horizontal, in a line, junior, later, level, linear,
   national, ordinal, phyletic, phylogenetic, posterior, progressive,
   puisne, racial, rectilineal, rectilinear, right, ruler-straight,
   sequent, sequential, serial, seriate, smooth, straight,
   straight-cut, straight-front, straight-side, streamlined,
   subsequent, succeeding, successional, successive, totemic, tribal,
   true, unbending, unbent, unbowed, unbroken, uncurved, undeflected,
   undeviating, undistorted, uninterrupted, unswerving, unturned,
   upright, vertical, younger



Bouvier's Law Dictionary, Revised 6th Ed (1856):

LINEAL. That which comes in a line. Lineal consanguinity is that which
subsists between persons, one of whom is descended in a direct line from the
other. Lineal descent, is that which takes place among lineal kindred.