I would plant boxwood in an L shape on the outside toward your property line framing the lilac.

Mulch the area and plant a variety of ferns, daffodils, black-eye Susans, and day lilies.

If you don't have deer in the area, you can plant hostas. It you do have deer, forget it. Deer love hostas.

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A naturalistic groundcover like Geranium 'Biokovo' or 'Karmina'.

I don't think the assessment that "it won't grow grass" is accurate. I say this because on the lilac side and the fence side of the mud strip, and all around elsewhere, there is grass growing. It would be more fair to say you're not doing the things required in order to grow grass in that particular spot. That said, if you wanted to grow additional plants, you'd need to create a bed for them to which grass is excluded. At the least, a bed should be created for the lilac, as no grass should be growing among its canes. IMO, the space is not begging for something to be added in order for the area to look better. What is begging is that poor lilac, which I really couldn't call a tree at this point. It's more like a scruffy, bedraggled bush. In order for it to become something someone would want to look at, it needs to be refined into a reasonably symmetrical and tidy shape. Here's a guideline that might help. I'm suggesting removing some top and side growth to help the canopy thicken up. After a shape is underway, you can allow it to grow a foot or so higher (whatever it is willing to do without scraggliness) every year.

Take a look at nearby trees and see if they don't need some of their lower limbs removed, which could help considerably in allowing more light to get to the lawn or other lower growing plants.

thank you....great advice!

The lilac looks scraggly because it is in too much shade. Pruning is not going to help that and that is not how a lilac is pruned anyway. Never from the top down but rather from the bottom up, removing the oldest canes at the base of the plant. Lilacs do not have a uniform growth habit or neat tidy, appearance and it does not improve the plant to force it into one. If you want that look, pick a different plant.

The lack of grass growing behind it looks to be more of a traffic issue than anything else, although neighboring trees and shade are contributing factors. When the photo is enlarged, you can clearly see how the grass along the fenceline starting from the road is tramped down by someone using it as a regular pathway or shortcut. Block off the access, apply a seed patch in the bare areas and it should fill in nicely.

Many times, the questions posed here have little to nothing to do with landscape design but are basic gardening/horticultural issues about plant care. This is one of them.