All normal rules apply for the river. You just can't stay in it at the end of your turn, unless you are the kraken.
So 3 lizardmen and 2 ogres.
This answer is not correct. River require only 1 token to conquer normally so you would only need 2 lizard men or 1 ogre to conquer 1 kraken in a in a river though it should also be noted that Lizzardmen have a ability which explicitly allows them to bypass river spaces so they would have no real need to attack the kracken.