The idea that women are generally better at cooperating hasn't been pulled out of thin air, there is actually a fair bit of evidence to support it. The idea as I understand it is that women > men at communicating and cooperating so bringing together an emergency all female cabinet to resolve a complex toxic failing negotiation will be more effective than a male/ mixed sex cabinet.
However, this is one of the times when we are actually interested in gender rather than sex, because the idea that women are better communicators/ cooperators is, as someone else pointed out, a gendered stereotype. It may also be true to a degree, but that's a result of female socialisation, not some magic female cooperation gene. So what Lucas should actually be looking for is a cabinet full of the best cooperators, who are least likely to exhibit masculine grandstanding and power grabbing. Given the current gender expectations of men and women, such a cabinet would probably contain more women than men, but may also contain men like Grieve and exclude women like Widdecombe. My (long winded) point is that what Lucas means when she says she wants an all woman cabinet is that she wants a cabinet full of people who behave in a certain way most commonly associated with people socialised female.
Anyway, like others have said it's never going to happen and it's dumb anyway because it misses the point by about a million miles over why Brexit is actually happening. A no deal Brexit isn't on the cards because of a lack of skilled male negotiators, it's on the cards because a lot of very wealthy people have a financial interest in it happening. The idea that if we'd just had a better team of people involved in negotiating a No Deal Brexit wouldn't be happening is so so naive. No deal was always the goal, right from the start.
As for the "your fantasy cab is too white" comments, that also misses the point spectacularly. The point is to bring together the best cooperators. Lucas believe sex is relevant in that equation so she's assembled a cab based on sex. She clearly doesn't think race is relevant to that equation, so why would she consider the race of the women in her cab? It's not like she only reached out to white women because she thinks white women are better cooperators than WOC. Now, if you said that she should include WOC because their perspective is valuable for representing the different demographics in our country then yes, that'd be a fair point. But if your goal is to fairly represent the demographic of our country then you would also have to include men, so the argument fails on every level.