Leucothoe gets eight leaf spot diseases and we cannot identify the disease from your photos.  It is very difficult to identify these diseases even when dealing with a plant sample.  Leucothoe is very difficult to grow in a garden setting without getting some kind of leaf spot.  It prefers woodsy settings and moist soil and is not at all fond of the wild swings in moisture that we have had in the past few years.  It can take time to get established.  We do not have data that would say which fungicide would be best.  If  you want to try a fungicide, first try a copper product in the spring.  Even if you use a fungicide, you may continue to get leaf spot especially in wet years.  vw