We were the kings and queens of promise

Aside from his secret identity trauma with Vash, Lelouch actually is interested in Vash. Vash's ability to handle the seemingly violent Rhode without resorting to violence himself is something Lelouch admires. He's also not sure what to make of the whole "the Stampede" part of Vash's name. Vash also seems like an all-around easy going guy and Lelouch likes seeing that in people, so long as it's not accompanied by naivety.