Born an empireth to a society that persecuted all aliens, but empireths in particular. Simply being one was to have a death sentence. Her father told her all of the old myths about the Superman as she grew up and she became steeped in the belief of a power greater than her that was guiding her life. Her faith was destroyed when her father was murdered by a Kandorian.
After that, she began to dream of Superman. They were visions that connected her to him. She called to him and he appeared, broken and exhausted. She nursed him back to health and brain-washed him to believe he was a low-level official working for the Kryptonian government and that Krypton had never been destroyed. She made him believe he was nothing more than a nobody in a menial job with no future and no dreams. She infused him with her own frustrations about the futility of existence.
When she was ready, she stole his powers and used his connection to the real world to break out into the Fortress of Solitude. She flew to Metropolis, wanting to have people worship her, only to discover the real truth: Superman wasn't a god at all, people didn't worship him, he'd earned their love and trust but no more.
When Superman and the group of alien Kandor rebels arrive to confront her, she fights back with the powers she stole from him. She stops Preus from killing him but blows both Preus and herself up in an attempt to protect Superman. Her current whereabouts is unknown but Superman believes she survived and will come back one day.
As an Empireth, every cell of Lyla's body is psychic, granting her a variety of abilities. She is telepathic, able to read minds, gather and alter memories (on a large scale considering she was stated as being able to mindwipe all of Metropolis if she felt like it), and also project incredibly strong and real emotions into them. She can also filter a person's perception of the world so they experience things how she wants them to, and is capable of keeping this up for an as yet undetermined amount of time (she did it to Superman for days without effort). At her normal level of power she is capable of making realistic constructs of humans and at her later levels of power she could make convincing constructs of many of Superman's foes including Doomsday. There may be a measure of belief needed to sustain the constructs as Superman was unharmed by the ones he knew were fake (though they could still affect the environment as if they were real). The psistructs are linked to her mind and destroying them causes her pain. She can make not only living constructs, but seems to be able to alter matter (possibly reality) as well, once plunging Metropolis into darkness and having tentacles come from the ground and destroy the city. Possibly the greatest ability Lyla possesses though is somethinger her people call "The Cistern." It allows her to fully copy the abilities of another being and retain them.
In addition to her psychic powers, Lyla has all of Superman's powers thanks to the Cistern. This makes her as strong, fast and durable as him with flight, laser vision and the rest of his abilties. She also gets stronger in the sun like he does, which not only increases the powers she took from him, but her natural ones as well.