Good evening JJ and thank you for reaching out to ask2.extension.

Personally I have not seen Pseudocercospora.  Did you test for it?

For disinfecting your tools I would suggest after you trim the dead out of each bush I would disinfect.  Just cut out infected branches.  If you trim anymore, disinfect before you trim healthy branches.  Be sure to destroy them. 

I would suggest to goggle how to treat for Pseudocercospora and the University of Iowa has a good article on the disease.

They talk about a fungicide treatment in the spring.  ”If repeated severe infections occur, preventative spring fungicide applications may help prevent disease. However, no fungicides have been specifically tested for leaf spot on Japanese tree lilac. Pseudocercospora fungal leaf diseases on ornamental plants are controlled with fungicide applications in the spring- starting when the leaves first emerge from the buds and repeated every 14 days (or however the label instructs) through the rainy period of spring.”

If you use a fungicide, please follow label instructions.

I’m not much help, but the website can give you better instructions.  I wish you good luck!