Spinel lithium manganese oxide (LMO) is a promising cathode material for Li-ion batteries. Dissolution of manganese from LMO into the electrolyte, however, limits its cycle life. The widely accepted mechanism of dissolution requires charge disproportionation of Mn(III), but the atomistic details of such processes have remained elusive. The dissolution has also been loosely correlated with the Jahn-Teller activity of Mn, especially when LMO is over-lithiated. Using first-principles simulations, we provide insights into the mechanism of both Jahn-Teller activity and disproportionation and discuss possible connections between the two.