I think you will need more boxes, and not only for Lulu.

Whenever I bring a new cat in the home, it takes some time for everyone to sort out their hierarchy. During that time, some "bully" cat can sprawl in front of the opening of boxes which are lined up, preventing a newbie from entering to use it. (Vita did this.) Also, some kittenish cat can pose on the hood and attack anyone who enters and is "busy." Crystal STILL does this, she is almost 2!

I had always heard the rule one box per cat plus one, if you scoop just once per day. I have 7 boxes, spread out among 3 different bedrooms.

Oh, another thing. Do you and your cousin use different brands of litter? Do NOT change the type of litter at the same time of the move, it is too much upheaval for them. So if you 2 are using 2 litters, you should have boxes with each type of litter available.

Cats can be very chosy about their boxes. With or without hood, type of litter, use a liner or not. Location. Privacy.

Amber would ONLY use Tidy Cats scoopable litter. Any other type, he refused to use the box at all.

This move is going to be a big deal for all the cats, not just your cousin's cats. It will take up to 2 seeks for them all to even accept one another. Good luck!