  Dark Matter (DM) theories and mass-tracing-light theories like MOND are by
construction nearly degenerate on galactic scales, but not when it comes to the
predicted shapes of Roche Lobes of a two-body system (e.g., a globular cluster
orbiting a host galaxy). We show that the flattening of the Roche lobe is
sensitive to the function mu(g) in modification of the law of gravity. We
generalise the analytical results obtained in the deep-MOND limit by Zhao
(2005, astro-ph/0511713 and astro-ph/0512425), and consider a binary in the
framework of a MOND-like gravity modification function mu(g) or a general
non-Keplerian gravity g \propto R^-\zeta. We give analytical expressions for
the inner Lagrange point and Robe lobe axis ratios. The Roche lobe volume is
proven to scale linearly with the true mass ratio, which applies to any mu(g),
hence mass-tracing light models would overpredict the Roche lobe of a DM-poor
globular cluster in a DM-rich host galaxy, and underpredict the size of a
DM-richer dwarf satellite. The lobes are squashed with the flattening ~ 0.4 in
the strong gravity and ~ 0.6 in the weak gravity; a precise measurement of the
flattening could be used to verify the anisotropic dilation effect which is
generic to MOND-like gravity. We generalise these results for extended mass
distribution, and compare predicted Roche radii in different gravity theories
with limiting radii of observed globular clusters and dwarf galaxy satellites.
