Can the Lion Stronghold be used on the defense to burn Kisada's negation or since the Lion has no attacking characters does it not change the game state?

You control no attacking characters. Therefore, it has no potential to change the game state.

To be precise, the game state will be changed because as the stronghold will now be bowed, but an action doesn't check changes caused by paying the cost, so effectively, no, you can't initiate the stronghold action while defending.

Yeah, you only take effects into account when checking the legality of triggering an ability.