They can get Powdery mildew, and as no one has answered you I found this on the RHS site.
"Powdery mildew:
Both powdery mildew species initially grow over the leaf surface, visible as a white powdery coating
Later, underlying tissues go brown and die
Unusually for powdery mildew infections, the brown tissue then drops out, often leaving irregular holes in the leaves, and tattered edges which look more like insect damage than disease.
Control

Non-chemical control:
Little can be done by cultural means to prevent infections when conditions are suitable. Plants usually grow through the problem, with new leaves being unaffected when growing conditions change
If the attack is very unsightly, consider clipping to remove affected leaves and encourage new growth. However, avoid heavy pruning as this will stress the plants and may aggravate the problem
Feeding may be helpful, although laurel is usually robust enough not to require it.

Chemical control:
Fungicides containing difenoconazole (Westland Plant Rescue Fungus Control), myclobutanil (Doff Systemic Fungus Control and other formulations), tebuconazole (Bayer Garden Multirose concentrate2) and triticonazole (Scotts Fungus Clear Ultra and other products) are approved for use against powdery mildews on ornamental garden plants and would probably give useful incidental control of shothole fungi as well, although this is not claimed by the manufacturers.

Plant and fish oil blends (Vitax Organic 2 in 1) and sulphur with fatty acids (Scotts Natural Fungus and Bug Killer) can be used on all plants against powdery mildews but are unlikley to have any incidental effect on leaf spot fungi or bacterial shothole."
Hope this hels