Luka has finally made her debut in Honkai Star Rail 1.3 update as a playable character, and so will her companion quest called "Mo Cuishle," which you will be able to complete to get free rewards like Stellar Jades, Trailblaze EXP, Credits, and more.
However, you will have to unlock it after completing Trailblaze Mission "Jarilo-VI — Silent Galaxy" and then interacting with Seele and Oleg (NPCs) in Boulder Town. Once you have done it, here is how you can complete Luka's companion mission in Honkai Star Rail.
Honkai Star Rail Luka Companion Mission: How To Unlock & Complete
After you have unlocked Luka's companion mission, Mo Cuishle, you will have to go to the location marked on the map and talk to Oleg and Selee. After completing a dialogue with them, go to the Fight Club at the location marked on the map and watch Luka defend his title.
Complete a short cutscene and a series of dialogues, and then, talk to Luka again to start his trial. Select your party, and a series of dialogues will begin automatically. Complete it and then, find Cassidy's robot friends.
You will have to do it using a drone that you will find in front of you. You will then be tasked to fix the drone by completing the Magflow Link puzzle, and you can find its solution below.
Little Fay will start flying again, and you will then have to follow it to find Big Ben's whereabouts. Complete another series of dialogues, and a battle against the enemy will begin. Complete a short dialogue and then, follow Big Ben, and it will take you to Cassidy.
Talk to him and then go to the next location to defeat the enemies. After a couple of battles, talk to Selee and Luka and find Svarog by going to the next marked location on the map. Talk to him, and after that, you will be tasked to beat him, and you will only have Luka this time.
However, Luka will fail and faint. He will then find himself in a clinic, and a series of dialogues will begin. After completing them, go to Oleg and ask about Luka. When you don't get all of the answers, he will ask you and Selee to sort everything you.
You will then receive a message from Selee to tell you that she has found Luka and she will ask you to go together. Find Selee and then follow Luka; however, you will have to keep hiding in the highlighted places to make sure that he doesn't see you.
A cutscene will eventually begin, and you will see Luka near a case. You and Selee go and check it out after Luka leaves, and you will see multiple drawings. You will then head back, and the quest will be completed.