Yes, he's liable. Here's one reason why.
Everyone agrees that a third-party rodef ("pursuer") is not subject to kim lei bideraba minei (apply the greater punishment), as the rodef is not "liable to the death penalty." Rather, we do whatever is necessary to save the "pursued", with lethal force authorized only if needed. The bystander who shoots in the heart when he could just have easily shot the rodef in the leg (let's assume this is an absolutely expert marksman) is considered a "murderer."
The more interesting question is if we look from the "pursued"'s perspective: we also find the rabbinic phrase -- haba lehorgecha, hashkem lehorgo -- if someone is out to kill you, kill them first. Many Achronim take that to mean that there is more authorization for lethal force to protect yourself than there is to protect a third party.
THEREFORE: Rabbi Akiva Eiger asks a related question in drush vechidush. The Torah says that if one man strikes another; if the victim dies, then it's murder and liable to capital punishment. If he lives, then the aggressor just pays for damages. Asks Rabbi Akiva Eiger: so Joe is standing there with a knife yelling at Bob, "I'm going to kill you!" If Bob is completely authorized to defend himself with lethal force, then Joe is deserving of death; therefore if the stab wound is non-lethal, why must Joe pay? Kim lei bideraba minei! Rabbi Akiva Eiger therefore rejects the premise that hashkeim lehorgo is any different than standard rodef, i.e. you are obligated to use minimum force in exactly the same way whether you are defending yourself or another. Because you are obligated to not use lethal force unless absolutely necessary, we don't consider a rodef to be "liable at this moment to the death penalty."
Later Achronim (IIRC R' Chaim Ozer Grozinski?) reply that the law of hashekm lehorgo is not so much an authorization for lethal force in the case of self-defense, as much as psychological exemption (ones rachmana patrei) as we can't demand people think that carefully with a gun in their face. But either way, the "pursuer" is not currently doing something that is "punishable by the death penalty" per se; hence, kim lei bideraba minei does not apply.
