That's actually a lichen on the tree, it appears to be one of the many species in the Foliose family of lichens but it also has a lot of similarities to certain species of the Fruticose family of lichens - but I don't know which one it is because there are so many of them.
Generally lichens are actually useful to have in any environment and quite beneficial to have growing on trees and don't harm trees. They are not pathogenic and to date there is no known control method to use on lichens. They are compatible growing on healthy trees since they are not parasitic or harmful on plants and don't take nutrients from them, the lichens mostly get their nutrients from the air and from moisture and already dead organic material in their environment.
But lichens will also grow more profusely on trees and plants that are already dead or are really sick and dying and usually beyond recovery. So I'm thinking that the reason why that lichen is growing so thickly on your crape myrtle is because your tree was already dying long before the lichen found it, the tree isn't dying
because of the lichen.
Here is some information that explains about lichens and may help you to understand what lichens are, how they are beneficial to the environment, and what you're dealing with. There are several pages to the second link and it also has photo galleries of several of the lichens in the three categories Crustose, Fruticose and Foliose lichens. The photo galleries might help you to identify the species growing on your tree. You can also do an image search online of lichens to try to find the name and type of the lichen you have on your tree.
https://plantclinic.tamu.edu/2014/04...ng-your-trees/
https://www.fs.fed.us/wildflowers/be...ns/about.shtml
I'd suggest you remove the branches that are already dead or are obviously dying and try to treat the tree for whatever disease it has if you wish, and if you can discover
what the disease is (it could be old age) and frankly I think your tree is already toasted - but I doubt that it is the lichen that is responsible for the disease or making it get worse. It's just growing on the surface of the dead and dying stuff. If you can identify the type of lichen you have you will get a better idea of how you might be able to get rid of the lichen if you aren't ready to cut down the whole tree yet.
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