The tree in question has teeny tiny leaves which turn brown and begin dropping in mid August [ zone 9] The tree was here when I moved in and must have been her for 40 or more years.It's many boughs add lots of dappled shade which I enjoy in this hot summer climate
Yes, and it is called Ulmus crassifolia! This link will give you information on the tree:
There are few leaves on our young trees. The trees are about 12 foot tall and leaves are very sparse.
Unfortunately, your photos did not come through. I am unable to see what is going on with your trees.
These symptoms sound like it could be a few different possible causes. This could be due to low soil nutrition, low sunlight, or a soil pH that is too far out of place.
https://www.gardeningknowhow.com/ornamental/trees/elm/lacebark-elm-information.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/making-sure-soil-drains-well.htm
One of the Lace Bark Elms that I planted 2 years ago seems to have stopped growing though it leafs out beautifully each year. It's approximately 3 feet tall has a beautifully full canopy but looks like it is an overgrow bonsai compared to it's mate. They were the same size when planted and yet the short one hasn't grown more than an inch since then while the other has shot up considerably; same ground, planting techniques and maintenance for both. Is there anything I can do to encourage it to grow taller?
It does look like a miniature tree! I suggest collecting a soil sample and getting it tested. You can do that at your local Extension Center. Also inspect the leaves and stems for signs of insects. Is the soil compacted? Do you fertilize? The article below says to use a slow release, high nitrogen fertilizer twice a year.
Here is info on their optimal care that should help:
https://www.gardeningknowhow.com/ornamental/trees/elm/lacebark-elm-information.htm