We live on a caliche/limestone hillside. We have one Texas Ash in the back yard and we really like it. I wouldn't call it fast-growing, however...at least, not in this kind of habitat. We also love the Bigtooth Maple we have in the front yard, which grows a bit faster than the ash does. But neither grew extremely fast.

I have a friend who grows a lace bark elm west of the Pedernales on HAmilton Pool rd, but she has a big layer river bottom that got trucked in so it is not a good comparison. How about Red Spanish oak or cedar elm.

None of the elms will be evergreen. But the Cedar Elm will be a better choice. They are much tougher and more drought tolerant than the Lacebark. I just planted one this year and it has sun scald. Since then I've noticed many around town that appear dead. Even some I know are on sprinkler systems! The cedar elm will not have a problem with the rock.

Another suggestion is a pecan tree. They can also tolerate limestone bedrock.

Another fast growing tree to consider is a Bradford Pear. I never used to like these...but I now live with one and it is the first tree to leaf out each spring and provides thick shade all summer. It is planted in heavy caliche/limestone/clay.

Pecans will not do well high and dry on a limestone hill. It has been my experience that they like a deeper soil and more moisture than what flows by on top of a hill. Cedar elms are tough But mine has lost its leaves. I am still waiting. I did not water it. since I don't have a lot of water.

Folks, thank you all for your responses. I really appreciate it. I agree with most of your assessment that Lacebark is not as tough as Cedar Elm. However, would it be correct to say that the Cedar elm is a slower growing tree than the Lacebark Elm?
I just think the Lacebark Elm is a very pretty tree!