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.
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            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).
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            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.
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   Lineal measure, the measure of length; -- usually written
      linear measure.
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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