A lamp has LED sources that are placed about a lamp axis in an axial arrangement. The lamp includes a post with post facets where the LED sources are mounted. The lamp includes a segmented reflector for guiding light from the LED sources. The segmented reflector includes reflective segments each of which is illuminated primarily by light from one of the post facets (e.g., one of the LED sources on the post facet). The LED sources may be made up of one or more LED dies. The LED dies may include optic-on-chip lenses to direct the light from each post facet to a corresponding reflective segment. The LED dies may be of different sizes and colors chosen to generate a particular far-field pattern.