The Luminary's species were a race of telepathic beings with bulbous heads and no mouths. Their technology was extremely advanced by Human standards, incorporating biological components as well as very small ships that were larger on the inside (using the "fifth dimension").
To repair failing systems, members of the Luminary's species visited Preplanis to steal the brain of Dr. Smith or one of the Robinsons. Their efforts were foiled when Will's grief over being taken from his family overloaded their computers. ("Invaders from the Fifth Dimension")
The Luminary's species were not referred to by name. One of their representatives is referred to as "Luminary" at the Internet Movie Database. It seems to have been intended that these aliens were disembodied heads, but their hands are clearly visible. In publicity photos, form-fitting black bodysuits can be seen while the actors strike menacing poses.