Doctor Light and the Light throughout their sinister careers paralleled one another's pathetic ploys towards power, and this included their each tied to Leagues. For Earth-One's Doctor, it was his mortal enemies of the Justice League. For the Light, it was his criminal organization known as the Octopus League. Utilizing their various nefarious gadgets and schemes, this drew them ones more into conflict with their old adversaries, costumed crusaders of the Justice League and Justice Society!
It is interesting that during this encounter with Starman, the Light obtained the hero's Gravity Rod which possessed similar levels of raw power in much the same manner as had the light-ray gun used by Arthur Light. Each of the Lights took to The seas for grand thefts that would by stymied by their heroic opponents.
After the Lights manipulated matters with their various devices, they used a myriad of mirrored images... be the the Doctor's holograms or the Light's henchmen.
Nevertheless, these nefarious nemesis of Justice were ultimately captured by their arch-enemies. Would they reappear again after such devise defeats? Absolutely... yet each time they'd fall short of their lofty aspirations. They may have reached for the stars, but their light was eclipsed time and time again.