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This likely is a case of improper pruning.
When people do this it causes lots of fast growing shoots to grow out of the main stem, and these shoots are not strong enough to hold themselves up.
https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/pruning-crepe-myrtle-trees.htm

I suspect water deficit and/or nutrient deficiency.
Soil fertility and water management are vital for plant health and flowering.

Water a wide area not just near the tree trunk, cover the absorbing root zone which spreads as far as the foliar canopy and more. Water deeply to wet the soil a minimum of six inches, preferably to 10 - 12 inches. Check this two to four hours after watering by digging down in a couple of spots to see how far the water infiltrated. Mulch the soil surface to help retain soil moisture.
Fertilize with a slow release complete organic fertilizer.

https://www.domyown.com/dr-earth-organic-all-purpose-fertilizer-p-9485.html

This is, actually, quite normal for most of these shrubs. You can't stop this from happening, but you can cut off these dead blooms. This can help encourage a second flush of flowering in many cases.

This article will give you more information on the care of these shrubs: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/crepe-myrtle-care.htm

Crape myrtles are generally cold-hardy to USDA Zone 7 or possibly 6, depending on the cultivar. They bloom on the current season's growth, so some gardeners in cooler zones try their hand at growing them as perennials.

Deer normally stay away from Crepe Myrtle, but a hungry Deer will eat anything.

https://www.gardeningknowhow.com/plant-problems/pests/deer/deer-repellents.htm

Hi Laura, Without photos we will have to accept your assessment and identification of the growth as lichens. This is normally not considered a parasite or disease condition, although susceptibility can be a result of weakening of the plant defenses from other issues.
The previous dieback and branch loss could be from water deficit (drought stress) and/or nutrient deficiencies or pest infestation, and not a direct result of the opportunistic lichen.