Substrates and packages for LED based light devices can incorporate a material with high thermal conductivity in at least the lateral direction (e.g., graphite or graphene) to spread heat across the surface of the substrate. A substrate or layer in a multi-layer substrate can have a graphite core disposed between ceramic sublayers that provide electrical insulation and thermal conductivity in the transverse direction. Another substrate or layer in a multi-layer substrate can be fabricated using a composite of graphite and ceramic materials.