Q.Will lilac bushes grow in Texas?
Is Texas too hot in the summer to grow lilac bushes?

You need a lilac variety that is heat tolerant and accepts mild winters. Here is an article that provides suggestions on lilac varieties to try and some alternatives to lilacs you may want to consider:
http://thedailysouth.southernliving.com/2009/04/17/is-the-south-too-hot-for-lilacs/
For tips on growing lilac bushes, please visit the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/lilac/lilac-care-growing-and-planting-lilac-bush-plants.htm