  Precision modeling of M dwarfs has become worthwhile in recent years due to
the increasingly precise values of masses and radii which can be obtained from
eclipsing binary studies. Torres (2013) has identified 4 prime M dwarf pairs
with the most precise empirical determinations of masses and radii. The
measured radii are consistently larger than standard stellar models predict. We
have previously modeled M dwarfs in the context of a criterion due to Gough &
Tayler in which magnetic fields inhibit the onset of convection according to a
physics-based prescription. New constraints on the models of M dwarfs are now
provided by measurements of lithium abundances. The key aspect of Li in terms
of setting constraints on magnetic modeling is that Li burning starts at T =
2.5 MK, and temperatures of just such magnitude are associated with the base of
the convection zone: magnetic inhibition of convective onset can shift this
base slightly closer to the surface, i.e. to slightly lower temperatures,
thereby reducing the amount of Li depletion compared to a non-magnetic model.
In the present paper, we consider how our magneto-convection models handle the
new test of stellar structure provided by Li measurements. Among the prime
systems listed by Torres, we find that plausible magnetic models work well for
CM Dra and YY Gem but not for CU Cnc. (The fourth system in Torres's list does
not yet have enough information to warrant magnetic modeling.) For CU Cnc, we
suggest that the observed lithium may have been accreted from a circumstellar
disk. We find that our magneto-convection models of CM Dra, YY Gem and CU Cnc
yield results which are consistent with the observed correlation between
magnetic flux and X-ray luminosity.
