Without being able to see your plants in person, I'll make some suggestions as to what it might be. Powdery mildew is an option, though not typically on lantana that is grown in full sun. Lantana is very susceptible to spider mites, and a severe infestation could cause that appearance to the leaves. Also, lantana lacebug is becoming more and more of a pest. They can certainly cause some serious issues for this plant.

Do a mite search and a lacebug search to see if either of these are the problem.

When I dont know what to do I mix a few drops of dish detergent with water and spray on the plant.It will not hurt the lantana,but it might get rid of the pest.Hope this helps.applepatch