It's a Lantana of some sort--the plant, not the disease. I've seen Lantanas chewed but not with foliage disease. Is there something above it dripping something down upon it, or are there holes in the leaves too? There's a lantana leaf miner...

Lantana are tough as nails except for frost.

Here is a link that might be useful: Lantana info

No, there's nothing dripping down and no holes... it's wierd. Here's a closer pic of the top & bottom of the leaves. Thanks for ID'ing the plant, I'll follow your link to look for answers.

Could it be possible that something toxic was splashed on this plant? I have never seen spots like that on a lantana.
I'd just cut off the affected leaves and see what happens. Min

Entomosporium leaf spot.

I would guess that you are probably either in a coastal zone or that the lantana is in considerable shade with evening irrigation.

Rarely causes serious damage to plants, however unsightly it may be.

Solution: keep irrigation off leaves, or try to water under conditions in which the leaves can dry quickly.

Yes, looks like it is in kind of a shady spot. Lantana likes a decent amount of sun.