From a standpoint of orbital mechanics / energetics, the most efficient way to capture an asteroid in a lunar orbit would be to first have it come very close to Earth, perhaps even aerobraking it in the upper atmosphere (must be very careful to not bring it so low that aerodynamic forces break it apart) and having the outbound trajectory bring it past the Moon, at which point the tug slows it down for lunar capture.
In practice, this is a terrible idea -- one small error and it could intersect Earth with potentially disastrous results. Instead, depending on how rapidly we can accelerate the asteroid, it would make the most sense to go straight into lunar orbit from the first pass. I doubt it would be possible to do that with current technology though, since that requires a large change in velocity in a very short span of time. Instead some trade-off would probably be made with the asteroid first being captured around the Earth at a comfortably large perigee distance, then over subsequent orbits bring it over to the Moon for final orbital insertion.
