Local Medicaid Enforcement Incentives Act of 2014 - Directs the Secretary of Health and Human Services (HHS) to establish a grant program to provide states with funds to: (1) detect and prevent Medicaid fraud, waste, and abuse; (2) recover overpayments to individuals or entities receiving Medicaid funds that result from such fraud, waste, or abuse; and (3) share with localities within the state that assist in such detection and prevention, or the recovery of such overpayments, at least 50% of the state's share of the total overpayments recovered during a period, minus administrative costs.