You’ll still pay all costs for a legendary spell you cast this way, including additional costs. You may also pay alternative costs.

Kethis’s last ability doesn’t change when you can play the legendary cards. For example, if you have a legendary creature card in your graveyard, you can cast it only during your main phase when the stack is empty. If you have a legendary land card in your graveyard, you can play it only during your main phase and only if you have an available land play remaining.

Kethis’s last ability affects only legendary cards that are in your graveyard at the time it resolves. Legendary cards put into your graveyard later in the turn won’t gain the ability. If you play a legendary card and it returns to your graveyard, it won’t have the ability anymore.