The Escarpment Black Cherry Prunus serotina var. eximia (Escarpment black cherry) is a handsome plant whose range is limited to the Edward’s Plateau in Central Texas, so it is relatively rare. This link provides some interesting info about this plant.
It is difficult to diagnose a plant problem from just a description, but the NPIN Profile sheet (see above ) describes the tree as being"drought deciduous", ie it loses its leaves under dry conditions. So the drought may be a contributing factor, and your increased watering plus the recent rains may be enough for the tree to start showing signs of recovery. Be aware though that plants can suffer from over watering as well as from under watering. (see greenthumbarticles.com , and texasforestservice.tamu.edu ). Another source of help is the Travis County Office of Texas AgriLife Extension.
Have you considered letting your neighbor pay for a Certified Arborist to come visit your tree and make an analysis?