Lelouch Lamperouge is the estrella 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 anime 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.