The Collaborative International Dictionary of English v.0.48:

Lapdog \Lap"dog`\, n.
   1. A small dog which is or can be fondled in the lap.
      [1913 Webster]

   2. One who does the bidding of another; a servile follower.
      [informal]
      [PJC]

WordNet (r) 3.0 (2006):

lapdog
    n 1: a dog small and tame enough to be held in the lap