  We quantify the potential for testing MOdified Newtonian Dynamics (MOND) with
LISA Pathfinder (LPF), should a saddle point flyby be incorporated into the
mission. We forecast the expected signal to noise ratio (SNR) for a variety of
instrument noise models and trajectories past the saddle. For standard
theoretical parameters the SNR reaches middle to high double figures even with
modest assumptions about instrument performance and saddle approach. Obvious
concerns, like systematics arising from LPF self-gravity, or the Newtonian
background, are examined and shown not to be a problem. We also investigate the
impact of a negative observational result upon the free-function determining
the theory. We demonstrate that, if Newton's gravitational constant is
constrained not be re-normalized by more than a few percent, only contrived
MONDian free-functions would survive a negative result. There are exceptions,
e.g. free-functions not asymptoting to 1 in the Newtonian limit, but rather
diverging or asymptoting to zero (depending on their mother relativistic
MONDian theory). Finally, we scan the structure of all proposed relativistic
MONDian theories, and classify them with regards to their non-relativistic
limit, finding three broad cases (with a few sub-cases depending on the form of
the free function). It is appears that only the Einstein-Aether formulation,
and the sub-cases where the free-function does not asymptote to 1 in other
theories, would survive a negative result without resorting to "designer"
free-functions.
