Lelouch Lamperouge is the étoile, star of Code Geass and C. C.'s one of the most important characters in the show. The two of them have a important relationship that affects both of their lives greatly, but they haven't become a couple yet.
Shipping is a really common thing for animé shows. Code Geass has plenty of interesting ships, but I think that LelouchxC2 is the show's best shipping. Lelouch and Shirley are cute together, but Shirley's incredibly sweet personality is probably not the best choice for the dangerous Lelouch.
I think that Lelouch and C. C. are pretty much perfect for each other. They're pretty much equally flawed due to all the immoral stuff they chose to do. Both of them are near the same level of awesomeness. They both have a harsh, but heroic personality that's loveable and awesome instead of unlikeable and lame.
Another reason that Lelouch and C. C. belong together is that they have helped each other plus than anybody else has. C. C. gave Lelouch his geass power and was his most supportive and helpful ally. Lelouch treated C. C. with plus care than précédant people she met and he made her want to continue living her life.
A big question about Lelouch and C. C. is if they have a crush on each other. It's hard to tell with Lelouch due to his confused reactions when girls try to be romantic with him. It's clear that Lelouch cares about C. C. When he met up with his dad saving C. C. was a major importance to him. Getting rid of the Emperor and saving Japon was pretty much the most important thing in his life so him getting distracted about saving C. C. proves he really likes her. I don't know if he romantically likes her though.
It's really clear that C. C. has a crush on Lelouch. She wanted to die before meeting, but after meeting Lelouch she felt like living. C. C. betrayed her years long partnership with the Emperor and Empress, but she ended up liking Lelouch that much. Plus she risked getting hurt par Jeremiah in the season one finale to help Lelouch. She also kissed Lelouch and it was much plus meangiful than any other Kiss Lelouch has ever got.
global, ensemble I think that Lelouch and C. C. are anime's most awesome duo and I hope they become a couple.