Debbie

Thanks for reaching out.

Honeysuckle (Lonicera) can get a leaf blight, powdery mildew and multiple leaf spot diseases. Diseases are worse in wet years. The diseases on this plant are generally not destructive enough to warrant control measures. 

Try managing it culturally.
As with any disease issues, improving airflow and sunlight around and into the plant helps to keep the leaves from staying wet, which is when diseases become problematic. Thinning the shrub by selective pruning is recommended.

There are some varieties that are invasive - hopefully you don't have one of them. I've provided you a resource to check (under PennState Ext).

Hope this is helpful!

University of MN Extension, Bush Honeysuckle: https://extension.umn.edu/trees-and-shrubs/bush-honeysuckle

PennState Extension, Shrub Honeysuckles: https://extension.psu.edu/shrub-honeysuckles

PennState Extension, Shrub ID:  https://extension.psu.edu/shrub-honeysuckle-accurate-identification