Does Akito the Exiled have anything to do with Code Geass? Does it have anything to do with Lelouch and what happens after R2? I need to know whether or not they continue his story or did he become immortal from his father's code?
In a sense, it does relate to the 2 seasons but not as a continuation of R2, Akito of the Exiled is set between the 2 seasons of Lelouch of the Rebellion during the 1 year gap, in it Britannia is putting pressure on it's EU Front.

Now I haven't watched the series yet however from screenshots we see C.C in this wearing a white hood and a man who looks like Lelouch with Suzaku (having been made a Knight of the Round) going by a different name with one of his eyes covered. In episode 3 of the OVA series it's revealed that Julius Kingsley is infact a brainwashed Lelouch. The brainwashing however is somewhat unstable as "Lelouch" reappears briefly, also his Geass has yet to be sealed.