N’aura nul lieu is quite outdated. Modern French rather uses either n’aura aucun lieu or n’aura nulle part.

In any case, this is not a double negation example but just a split negative where both ne and nul(le)/aucun are used to negate "aura un lieu/aura quelque part" (i.e. will have "somewhere" vs will have "nowhere").

A real double negation would have been n’aura pas nul lieu: will have "no nowhere".

See: Why does French use a "split negative"?
Does `ne` and `pas` have a different meaning? Does "ne" not negate words that are already negative?