Local Energy Supply and Resiliency Act of 2013 - Requires the Secretary of Energy (DOE) to establish a program to disseminate information and provide technical assistance, directly or through grants, to assist eligible entities in identifying, evaluating, planning, and designing local energy infrastructure. Defines "local energy infrastructure" as a system that:

• recovers or produces useful thermal or electric energy from waste energy or renewable energy resources,
• generates electricity using a combined heat and power system,
• distributes electricity in microgrids,
• stores thermal energy, or
• distributes thermal energy or transfers it to building heating and cooling systems via a district energy system.

Authorizes the Secretary to award grants to provide funds to cover no more than: (1) 100% of the cost of initial assessment to identify local energy opportunities, (2) 75% of the cost of feasibility studies to assess the potential for the implementation of local energy infrastructure, (3) 60% of the cost of guidance on overcoming barriers to such implementation, and (4) 45% of the cost of detailed engineering of local energy infrastructure.

Amends the Energy Policy Act of 2005 to authorize the Secretary to make loan guarantees for commercial or innovative projects for local energy infrastructure under the existing loan guarantee program that provides incentives for innovative technologies.

Amends the Community Development Banking and Financial Institutions Act of 1994 to redefine "investment area" to include an area that has the potential for implementation of local energy infrastructure.