black soot on shrubs under lime trees

Skimmias are quite good in these conditions and may have died from other cuases such as coral spot fungus or botrytis, and drought would probably be a challenge too.

Other shrubs to try for shade would be aucuba, laurustinus, mahonia and sarcococca. But all of these would need regular watering to ge them to grow.

Evergreens are actually better in these conditions because they can grow during the time when the leaves are off the trees.