@Nuke: Why on earth should there be an anti-graviton? The Electromagnetic Force has no need for an anti-photon, so I hardly see why gravity should be any different. (FYI, supersymmetry is String and M-Theory, not QM. Honestly, I've never taken those two theories very seriously for the simple reason that, unlike General Relativity or Quantum Electrodynamic, they make no predictions which are actually testable.)
@bfobar: Just think of it like electromagnetism. You run electrical current through a wire and you create a cylindrical magnetic field. When you increase or decrease the current, the magnetic field generated will increase or decrease in intensity. Whenever the magnetic field changes, you induce an electrostatic field. As long as your magnetic field is stationary, there will be no electrostatic field. But as soon as the magnetic field starts changing, some electric field E is induced. Not sure it will help, but you might look at this:
http://en.wikipedia.org/wiki/Faraday%27s_law_of_inductionThis gravitomagnetism should theoretically behave the same way. With EM, your current is moving electrical charge. With Lense-Thirring fields, your current is just moving mass. Most talk I've heard about this effect, though, suggests that you'd need a "current" of matter as dense as the degenerate core of a white dwarf accelerated to an appreciable fraction of light-speed to get much of an effect.