Lelouch and Kallen
These two first meet, well, I suppose it couldn't really be called a meeting, but they encounter each other in a battle with the Britannian forces. In the first episode, Lelouch helps out the terrorist organisation Kallen is in.
They later meet again, but in a different situation. Kallen is in fact a classmate of Lelouch, who is often absent for "health reasons". Lelouch immediately recognizes her and sees past this pretense. He uses his Geass on her to gain information, but when trying it the second time on her, he finds Geass useless. Here is where he realizes that the Geass can only be used once on a person. This is also where Kallen starts suspecting Lelouch, and his possible involvment in the Shinjuku Ghetto incident.
Kallen finds herself a member of the student council, and at Rivalz's suggestion to celebrate, dirties her clothes with champagne. While in the shower behind curtains, Lelouch comes in to lends her clothes. Here she confronts Lelouch, grabbing him by the arm and getting out a knife ready to threaten him. However, manipulating Geass, Lelouch completely eliminates Kallen's suspicions by making Sayoko relay a recorded message. What is the significance of this? Well, Lelouch sees Kalen stark naked... xD That HAS to contribute to the relationship xD
Kallen's relationship with Zero, and Kallen's relationship with Lelouch should be seen as two completely different relationships. Lelouch's and Zero's relationship with Kallen differs on the outside, but on the inside, he perhaps cares a bit for Kallen, but most of his motives involve manipulation of her usefulness.
In episode 9, Kallen and Lelouch have a heart felt talk, where Lelouch says that many Japanese live by lowering their heads to the Britannians, simply because it's easier. This that annoys and offends Kallen, as it reminds Kallen of her own mother. She slaps Lelouch, a walks away leaving Lelouch with a mark on his face. Generally, Kallen doesn't think much of Lelouch. He's simply a classmate, and acquaintance, somewhat of a friend, but not really.
This contrasts completely to her view of Zero. While at first slightly distrusting of him, Kallen begins to worship Zero, to the point of being quite infatuated as well; his charisma and intelligence completely wins her over. She truly believes that Zero is doing everything he can for Japan. In short, Kallen would die for Zero.
While perhaps Lelouch does actually care a bit for Kallen, most of his attention to her is for her Knightmare piloting skill; her usefulness in the Order of the Black Knights. If Kallen were in peril, his first thoughts would be on losing a valuable chess piece, not a valuable friend. Nonetheless, he treats Kallen kindly and with respect.
