Assuming you want some height here, maybe an upright grass interspersed with perennials? This is little bluestem grass (native; blue/green in summer, turns a warm amber/rust color in the fall) with allium 'Summer Beauty' (could also add liatris or tall phlox). Another combination could be feather reed grass 'Karl Foerster' (golden in the fall) with threadleaf coreopsis and black-eyed susan. These will all be dormant in winter; their dried stems and seedheads will stand until beaten down by snow, will need cutting down in early spring (or sooner if you wish).

There are narrow evergreens if you want something more permanent ('Stonehenge Skinny' yew, 'Compressa' pencil point juniper, etc; google "narrow evergreen shrubs' for others). There are even narrow deciduous trees that would cast some shade (ginkgo, Japanese maple, etc.; google "columnar trees") if their roots can spread and get enough water (concrete won't let water through; can't see what's on the other side of the fence).

Others might have more suggestions, or ask a local nursery for recommendations.

How wide is that strip? Looks to be only 15 or 16 inches, in which case none of the plants suggested will fit properly or thrive even if you could shoe horn them in. And this is from 30 years practical experience as a designer.

If you want height, then go with some vines....something fairly flat and 2 dimensional. Otherwise, you are pretty much restricted to groundcovers or annuals.

I grow both grasses mentioned and the space is simply too small for them. A low groundcover, sedums, would work. Trees are completely out of the question.

If you really just want something green and growing there…sedums pack a lot of punch into a small space. It’s a low ground cover that spreads easily, tolerates poor conditions/drought, comes in all sorts of variations, flowers, and offers seasonal color changes…perfect for a small space like yours. Another option would be to lay river rock(or plant sedums)in the space and put plants in containers…that way you can add greenery/plants/small trees wherever you want in your outdoor space. Put them on casters and you can move them around and change your landscaping on a whim to suit your outdoor needs.

What's on the other side of the fence? Plenty of soil for the roots of any plants you put there? Or more cement? I'd put in vines. Without a clue as to your zone, it's hard to advise.

The other side is grass

If anyone can names of plants that would be helpful- rose bushes grow there, I tried lavender last year and that did ok, I tried morning glories and they didnt grow I think the soil lacks nutrients. its about a foot wide- Thanks

If the lavender did OK, why isn't that the solution?

You have roses and lavender. Looks like you got lillies popping up, might be fulvas or something else. You could put in more roses, lavender, and lillies. Other hearty perennial herbs like sages, thyme, and oregano could probably grow in there.

I was going to suggest mini roses, if the ones you have are doing well. Alternate with catmint, daylilies (whatever color you like, but look for rebloomers.) Anything you put there will need to like full sun but also heat reflecting off of the cement and possibly more alkaline soil, again the influence of the cement. Perhaps some pros could give more guidance about the soil conditons - but just avoid acid loving plants like azaleas.

I agree that basil, thyme, oregano, sage would be interesting (also edible and fragrant!)

Thank you- lavender got too big and I did not love how it grew. I will try some herbs.

Here are some plants that would coordinate and extend color over the length of the season: sage 'Caradonna', rose 'Flower Carpet Pink', alliums 'Summer Beauty' and 'Millennium', Phlox 'Jeana', and sedum 'Autumn Joy'. If it were my yard, I would think vertical and set up a trellis for clematis. You could also use some of the smaller catmints.

That space is super small and assumably hot with sunlight reflected back off the fence. Almost anything that loves those conditions will get too big and sprawl, as you discovered with the lavender.

A creeping groundcover is the answer, I think. It might sprawl a bit too but shouldn’t be in your way. Look in the sedum family for ideas. Here’s one.

But if your dog eats mulch, there’s no guarantee he/she won’t eat plants too.

If lavender got too big, then skip the sage- it too can get to be a larger plant. Thyme and oregano might be too unruly for you too- they don't get as tall as lavender and sage, but they can spread out and should be trimmed to keep them nice.

Can you post pics of the whole area? You can’t design landacape in a vacuum. It’s like asking what sofa would look good in a living room with the pic of only one wall.

There is not enough space for most thins. Tall narrow flowers would look good, such as sunflowers, orienpet lilies, dinnerplate dahlias. You can also consider planting a small vegetable garden there. It would be a good place for tall crops in a line such as corn or okra.