だが、主であるそなたの許可なくばそれも許されぬ…！
I understand it pretty much means "However, being our master, we can't even do that without your permission." but I don't get why なく and ば are both together. I would have said : "なく" or "なければ" but never "なくば". What could the explanation behind this be ?
なくば is an older form of なければ. It's not generally used in modern Japanese (outside of perhaps a few fossilised expressions like さもなくば), but is still recognised and can be used as part of an affected style of speech.
This character's speech is clearly somewhat archaic in flavour (as also evidenced by the use of そなた and the ぬ negation), so the use of なくば seems in fitting with that style.
