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.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Underlie \Un`der*lie"\, v. i.
   To lie below or under.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Underlie \Un"der*lie`\, n.
   See Underlay, n., 1.
   [1913 Webster]

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.
      [1913 Webster]

WordNet (r) 3.0 (2006):

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

Moby Thesaurus II by Grady Ward, 1.0:

65 Moby Thesaurus words for "underlie":
   afford support, back, back up, be latent, bear, bear up, bed on,
   bolster, bolster up, bottom on, brace, build on, buoy up, buttress,
   carry, couch, cradle, crawl, crouch, crutch, cushion,
   escape notice, found on, give support, ground on, grovel,
   hibernate, hold, hold up, hug the earth, keep afloat, keep up,
   lend support, lie beneath, lie dormant, lie hid, lie low,
   lie prone, lie prostrate, lie under, lurk, mainstay, maintain,
   make no sign, pillow, prop, reinforce, set on, shore, shore up,
   shoulder, smolder, squat, stay, subsidize, subvention, support,
   sustain, underbrace, undergird, underpin, underset, upbear, uphold,
   upkeep