A lamp has an optically transmissive enclosure and a base. A tower extends from the base into the enclosure and supports an LED assembly in the enclosure. The LED assembly comprises a plurality of LEDs operable to emit light when energized through an electrical path from the base. The tower and the LED assembly are arranged such that the plurality of LEDs are disposed about the periphery of the tower in a band and face outwardly toward the enclosure to create a source of the light that appears as a glowing filament. The tower forms part of a heat sink that transmits heat from the LED assembly to the ambient environment. The LED assembly has a three-dimensional shape. An electrical interconnect connects a conductor to the heat sink where the conductor is in the electrical path between the LED assembly and the base.