Are we sure dementia is not "hardware"? Or is it "software"? Or is that dichotomy meaningless in sufficiently complex "systems" (much less predictable and much more interwined than somewhat abstract and basic ones like computers, that are human-made attempts after all)?

Some flaws are due to the ship, some are in the captain. But when the captain is the ship, who knows for sure?

Plus, let we suppose the Dark Overlord has gone insane. Are you sure he's mad? Or is it only your opinion on its thinking as very non-human (which is what it wanted to become, after all)? To it, it's finally post-human (ahem, in a nietzchean classic-evil way, i.e. unsensitive steel titan tyrant from Dune prequel, not that he couldn't become some in a fully organic way...)

Lastly,in this form, it implies a paradox.
Even if it was safe to assume it's a purely abstract (mind-driven) fault and only a functional fault (insane and not unlikable to the evaluator)...the problem at that point would be the lich itself.
Its mind is making tricks on it and its pristine body and brain...lack of humanity does not bother it: it's a feature (soul is another component, if we want to be so analysing).
Moreover, it being a uber-cyber-lich, it has access to well hashed backup of its mind :-p (whatever mind is...) in a desirable state. But his(its) logic is broken in the first place, remember! Think of a wholly infected PC (e.g. by a rootkit). It has that backup but in this terminal state the Lich is certainly incapable of executing the replacement routine.