Maybe I’m going a little bit fast with the new space. Have you been switching out their living spaces – putting William into Lily’s and vice versa? They should get used to one another’s smells even more than just living next to each other. If so, then the next thing you want to make sure is that they aren’t fighting in neutral space – such as the bathtub. From what I read, they’re fine in the bath tub although I’m not sure how long of a session they’ve had. If they can stand each other for 30 mins to an hour, then it’s time for the next step that I mentioned. I’d probably put all of Lily’s things in there though (litter box, food dish, etc.) to give her a slight advantage to it being her space.
Here’s the thing though – you’ll have to leave them together 24/7. This is the biggest hurdle that we as rabbit parents have to go through as we know that they fight and that things can happen quickly but it is a hurdle we need to get over and do so with very little fear. If you’re afraid, your rabbits will sense it and become nervous themselves. Maryann used to attack Dono because she thought he was the threat that was scaring me.
There will be some fighting as dominance is worked out. In fact, there could be some fighting for the rest of their lives. Maryann still takes tufts of fur out of Dono about once a week (I actually caught her mounting him over the holidays). If a fight starts, the first thing to try is a spray gun. If that doesn’t work, use a book or something else and push it between them. It’s hard to watch but it is something that happens.
Another thing you could try is to turn both William’s and Lily’s cages into one big condo with a ‘door’ between the two. If William is living with Lily on HER turf, it might go easier.