I'm not claiming that Putin is acting irrationally, at least not any more irrationally than other leaders - after all, politicians are still human.

My question is why Navalny would have believed that it would not be rational for Putin to kill him.

Lenin entered Russia at a more advantageous moment than Navalny did. The February Revolution had already happened. The government was new. Navalny, in contrast, entered a Russia in which the government was stable and had been around for a long time.