[Note as of this revision: The answer below contains unmarked spoilers for s2.]
From what I remember: Lelouch and Nunnally were given as hostages to Japan. Britannia invades Japan. Lelouch and Nunnally somehow live.
Why exactly are they alive and not announced dead?
Here's what I understand:
The whole point of taking or giving hostages is to ensure certain agreements are kept. When Britannia invaded Japan, it seems whatever agreement Britannia and Japan had was breached and then Genbu or whoever should've executed Lelouch or Nunnally. Or well perhaps someone tried but failed, but I think that's unlikely.
If for some reason the relevant legitimate or de facto authorities of Japan didn't want to execute Lelouch and Nunnally (pity, morality, attempt at using them as double agents or whatever), then why weren't the deaths of Lelouch and Nunnally faked and announced (to show that Japan really does follow on its threats. Otherwise, in the future, people will not necessarily take Japan's threats seriously).
Could be remembering the series wrong, but it seems like they guessed Lelouch and Nunnally were dead rather than, say, found out from Japanese news. If I were 1 of the Britannian peeps, then I think I would find it suspicious that the Japanese authorities didn't execute or announce that they executed them.