My partner isn't diagnosed with anything but I suspect ND and he really struggles with motivation. Thankfully we don't have kids and I have ADHD so I understand the struggles to a degree so I don't really have any tips exactly and I imagine my experience won't be that relatable for you. I avoid labelling it as laziness (though he will call it that) because I don't think it's helpful and also it hand waves it away as something normal/a character trait rather than an avoidant coping mechanism which is what I think it is for him.
I'm also a little wary of excusing men not pulling their weight, we aren't having children but I do think if you have these struggles and choose to have kids without addressing them that's a very selfish move (from him, not you).
That being said, it does sound like this is something he's aware of as he's acknowledged it with the jokes and might be interested in exploring/understanding about himself. I'd personally be encouraging him to take some ownership of the issue and figuring out what will help him step up as opposed to tips to help you manage him better. There's a book called 'Laziness does not exist' which I found really insightful about the things people are struggling with that look like laziness but are actually often driven by things like undiagnosed ND. It probably sounds counterintuitive but I do think taking some of the shame out of it can make it easier for someone to see and act to change a behaviour. My worst traits are things I can't bear to address because I feel so guilty and ashamed of them.
That's probably not a quick fix though, so in the meantime, can he compensate financially eg by paying for a cleaner out of his salary? But again if it's down to you to do all the admin around that it seems unfair. My partner loves tech and earns more so if I can think of a techy solution he will research, buy it and set it up eg plumbed in robot mop/robot lawnmower/bean to cup coffee machine instead of pods. But it's still on me to actually run the robots eg pick things up off the floor so they can work (and that clutter is normally mine tbf)
A couple of things I do on the off chance it helps:
I take note of the few things that he will do without fail and let him do those even if I would prefer to do them sometimes. So he will happily just let the dog go un-walled for 6 months, but he has to eat, so if I leave him to sort dinner while I do the evening walk, it's ready when I get back and he normally leaves the kitchen cleaner than I do when I cook too. It's not a perfect solution because it means we eat less healthily than I'd like and he gets to opt out whenever he feels like it (a lot) by ordering takeaway, but it is better than having the mental load of planning and cooking every night.
It sounds like you probably already do this but I've also learned not to hope for help with anything that matters to me and just to make sure it's done. So eg petty but he will throw away coffee pods rather than empty and recycle them if he thinks I won't notice. So even though it's unfair because he drinks 10x the coffee I do and it hurts my hands to clean them out, I just try to do it every day and don't expect he'll do it it I leave them for him.