The Collaborative International Dictionary of English v.0.48:

Underlay \Un"der*lay`\, n.
   1. (Mining) The inclination of a vein, fault, or lode from
      the vertical; a hade; -- called also underlie.
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   2. (Print.) A thickness of paper, pasteboard, or the like,
      placed under a cut, or stereotype plate, or under type, in
      the form, to bring it, or any part of it, to the proper
      height; also, something placed back of a part of the
      tympan, so as to secure the right impression.
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The Collaborative International Dictionary of English v.0.48:

Underlie \Un`der*lie"\, v. i.
   To lie below or under.
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The Collaborative International Dictionary of English v.0.48:

Underlie \Un"der*lie`\, n.
   See Underlay, n., 1.
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The Collaborative International Dictionary of English v.0.48:

Underlie \Un`der*lie"\, v. t. [AS. underlicgan. See Under, and
   Lie to be prostrate.]
   1. To lie under; to rest beneath; to be situated under; as, a
      stratum of clay underlies the surface gravel.
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   2. To be at the basis of; to form the foundation of; to
      support; as, a doctrine underlying a theory.
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   3. To be subject or amenable to. [R.]
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            The knight of Ivanhoe . . . underlies the challenge
            of Brian der Bois Guilbert.           --Sir W.
                                                  Scott.
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WordNet (r) 3.0 (2006):

underlie
    v 1: be or form the base for
    2: lie underneath