Light emitting assemblies comprise a plurality of Light Emitting Diode (LED) dies arranged and attached to common substrate to form an LED array having a desired optimum packing density. The LED dies are wired to one another and are attached to landing pads on the substrate for receiving power from an external electrical source via an interconnect device. The assembly comprises a lens structure, wherein each LED die comprises an optical lens disposed thereover that is configured to promote optimal light transmission. Each optical lens has a diameter that is between about 1.5 to 3 times the size of a respective LED die, and is shaped in the form of a hemisphere. Fillet segments are integral with and interposed between the adjacent optical lenses, and provide sufficient space between adjacent optical lenses so that the diameters of adjacent optical lenses do not intersect with one another.