What is the lower bound for lightspeed?

I am investigating the possibility of modifying the speed of light in my world. Assuming that the speed of light in a vacuum can (and in my world, is) modified, what lower bound exists that would permit humanity to exist?

Everyone has probably heard at least once that some values in Physics must be so precise that it could be compared to [insert absurdly precise example]. So is Light fine-tuned?

What would be the lower bound for light speed which still allows Human live? In following questions I want to address an upper bound and most notable effects.

Thanks to many physicists we know that light speed is very important for any part of fundamental Physics (Gravitation, Energy, Relativity, ...) At some light speeds Atoms might have so much energy that 1g of radioactive material would be enough to wipe out all human life.

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What is the lower bound for lightspeed?

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