The difference is the same as that between 赤くない and 赤くはない, etc. As far as this は is concerned, there is nothing specific to double negation. は in a negative sentence can be an explicit contrast marker, but sometimes it's nothing more than a particle you use unconditionally in negative sentences.
は in 必要なくはない can carry a strong contrastive meaning (similarly to 必要ではある which is always strongly contrastive).
It's very expensive, but it doesn't mean it's unnecessary.
(は is mandatory here)
It's very expensive, but it is necessary.
When this contrastive meaning seems unimportant, you can think it's just a common and natural way to say "It's not unnecessary". In such cases, it's basically interchangeable with 必要なくない. Still, 必要なくない sounds colloquial, and you should use 必要なくはない in formal settings. I suppose most textbooks use なくはない almost unconditionally.