Luma as Superman's Lover
Luma first appearance was in Action Comics #289, June 1962, titled: "Superman's Super-Courtship!"
After seeing a romantic movie, Kara feel sorry for Superman, because he's alone without a lover. So she decided to be Superman's personal cupid, and tries to arrange him a few dates. But after trying with Helen of Troy and an adult version of Saturn Girl, she understand that Superman needs someone more like her. Therefor with the Fortress of Solitude's computer she search in the know universe a grown up super heroine. Kara finds Luma Lynai, the Superwoman of the far away planet Staryl.
They actually come to like each other. So Luma come to Earth with Superman, but only to realize that the Earth's Sun is deadly to her. Kal-El couldn't leave Earth, for the planet needed the Superman. So they break up.
Later Kara would realize that she should not interfere with Superman's romantic life.
Little is known about Luma, yet her powers appear to be very similar to the Kryptonian ones.
Like a Kryptonian Luma's power source his a star, only in her case an Orange Sun.
Only one weakness is known: a yellow star radiation. The yellow sun's light not only draws her power, but also harms her. It seems that the yellow sun will kill her, in the same way Kryptonite kills Superman.
JSA Classified #3: Power Trip, Part III (November 2005)
A grown up Supergirl with Luma's suit appears to Power Girl in a Psycho-Pirate 's illusion.
The Kingdom: Planet Krypton #1 (February 1999)
It is reveled that one of the "ghosts" seen in the empty "Planet Krypton" restaurant is in fact Luma Lynai.
Superman's Girl Friend Lois Lane #97: "The Three Super-Sirens!" (November 1969)
She appears in Superman's memories while he remembers long lost lovers.