Why do you have to get rid of the rose ? Just move it forward from the tree. The tree is the issue it is way to big for that space and will contiune to grow and need removal so my advice remove it now The grass is non existant anyway so why not dig it up get some nice perennials , no tree and bark mulch no grass Good weed barrier that allows the water to get to the plants .To choose plants go to the garden center to get help so you have something pretty all year round.. Since the neighbor has gras you will need to weed form time to time since their grass will migrate .If the rose gets enough sun keep it if not replace that too.

Unless the tree is 25-30 years old, it will continue to grow and it will be way too big for the space. I suspect you're going to need to get rid of it sooner or later. Move the roses. I would not bother to maintain such a small and patchy lawn. Plant some groundcovers, at the minimum, I like creeping phlox, but a mix of heaths and heathers are low-growing and can have different flowering times. These are usually evergreen, but might look a little brown and ratty if you have a cold winter winds with no snow cover.

No one can suggest plants as we don't know your climate. Perhaps you could coordinate with the neighbor to put in low growing evergreen ground cover plants.

I’m in NYC for reference

What kid of maple is it? That could determine how necessary it may be to remove the tree.

I like your neighbor’s tree.

Are you friendly with the neighbor? If so, talk about what you'd like to have there and make it one garden And not grass. Silly to have to mow something that size.

If you want low maintenance, "beach" strawberry has white flowers and vinca minor with periwinkle blue flowers. Both are spreading groundcover, fill in nicely and have lush green foliage. Plant all the way to the house.

Might want to think twice about planting a spreading or creeping ground cover. Or at least check with the neighbor if you consider planting some. It will spread to their side of the little fence. If they like their patch of grass, it might be greatly irritating to fight off your plantings. Or you may find you are not inclined to fight your plantings to keep them out of the neighbors side.

Okay then cover with gravel and rock and add some big pots with six-packs of seasonal flowers that change out every four months, Pink, yellow and purple in Spring, red white and blue in Summer, Orange and gold in Fall. Little evergreens in Winter...or year 'round with flowers around them.