Light-emitting die (LED) Lamps, heat sinks, and related methods are provided. An LED lamp can include a mounting substrate having a top surface, a bottom surface and side edges. An LED package can be disposed on the top surface of the mounting substrate with the LED package comprising an LED chip. The LED lamp can include a heat sink that can include a heat sink base and a spacer extending upward from the base. The spacer can have a mounting area or pad distal from the heat sink base on which the bottom surface of the mounting substrate is disposed. The spacer can also have a width that is less than a width between the side edges of the mounting substrate. The LED lamp can further include a lens disposed over the LED package and the mounting substrate.