The answer to that question is really quite complicated, when you account for the existence of girls both Super and Power across multiple eras. But I’ll do my best to untangle this for you. First, we’ll talk about Supergirl.
The Supergirl we know best as Kara Zor-El made her first appearance in Action Comics #252 (1959). But it would be a while until the world learned who she was — all early Supergirl stories take place at Middle Orphanage, where Supergirl lived under the identity of Linda Lee until she was ready for the world to know who she was.
The first encounter between Luthor and Supergirl was in Action Comics #275 (1961) — but that doesn’t quite count, because it’s an “Imaginary Story” where Kara first landed on Earth to be adopted by the Kents instead of Kal-El.
In Action Comics #279 that same year, Luthor finally learns of the existence of the Silver Age Supergirl — when she appears to break him out of prison. At the time, Supergirl was under the hypnosis of Lesla-Lar, an evil Kandorian scientist who envied Supergirl’s life and sought to live it by proxy.
Fast forward to Crisis on Infinite Earths (1985). Supergirl meets a tragic end at the hands of the Anti-Monitor, and is then erased from continuity when the multiverse is restructured at its climax. Superman is once again the Last Kryptonian.
In Superman #16 (1988), a new Supergirl appears — the Matrix Supergirl. This one was created by Luthor himself, in an alternate reality where Zod conquers the Earth, and the planet requires a new champion to rise up against him. At the end of this storyline, the post-Crisis Superman brings the Matrix Supergirl from this pocket universe into his own, where she spends a few years trying to find her place in this new world.
Sadly, Matrix Supergirl would find the wrong answer. In “Superman: Panic in the Sky” (1992), available in trade paperback, Supergirl first meets the Lex Luthor of this universe, who at the time was inhabiting a younger, fiery haired body and pretending to be his own long lost son. Reminded of the kind, Earth protecting Luthor of her own pocket dimension, Matrix Supergirl falls in love with the rejuvenated Luthor, who is quick to take advantage of her. She continues to operate as his agent throughout the Death and Rebirth of Superman story arc, and it’s some time before Matrix recognizes Luthor for the monster he is.
(Matrix Supergirl’s storyline from there on out gets pretty complicated, and falls beyond the scope of this particular question. Suffice to say she eventually becomes some sort of angel and ascends from this mortal plane. Then there was Cir-El, another Supergirl with an equally complicated backstory, but she was around for so little time that she barely counts. But if you’re really curious for their meeting, then read Superman/Batman: Public Enemies.)
Eventually, the original Kara Zor-El makes her post-Crisis debut on Earth in Superman/Batman #8 (2004). Not long afterwards, in Superman/Batman #19 (2005), a disgraced former President Luthor is seen testing the potential threat this new Supergirl might possess from behind the scenes.
Then, in 2011, continuity was reset with Flashpoint and The New 52, and Kara-Zor El makes her 3rd first landing on Earth in Supergirl #1. Luthor finds her once again in Supergirl #18 (2013), while monitoring footage of the Super-Family’s battle with H’el. Much like the Luthor of 1992, here Lex sees not a threat, but an opportunity.
Now, let’s talk about Power Girl. Power Girl was first introduced as Kara Zor-L, the Supergirl of Earth-2, in All Star Comics #58 (1976). When we first meet her, she’s already been operating on that Earth for some time, and has presumably already been acquainted with Luthor. Then comes Crisis on Infinite Earths. Power Girl migrates to Earth, and is retconned as not being a Kryptonian at all, but an ancient resident of the pre-submerged Atlantis, frozen in time until the present day. It’s not until Infinite Crisis (2005) where Kara rediscovers her true past as a Kryptonian refugee from another universe.
So, this is all to say that I’m afraid we never get to see a first encounter between Luthor and Power Girl. But if you’re looking to see his first impression of Kara, you’ve got plenty of options to choose from.