I'm pretty sure my Myer lemon tree has a fungus called "black sooty mold". I had this same problem a few years ago but was able to successfully treat it. It's pretty nasty and if left untreated, would likely kill my lemon tree.
This black mold usually forms due to an insect waste product (called honeydew) left on plants. Insects that cause this problem include aphids and mealy bugs, two common garden pests. Treating sooty mold is not a matter of simply removing the mold. For a long-term solution to this problem, you must get rid of the insects.
What I did employ one of my favorite products, Neem Concentrate from GreenLight, an organic insecticide, fungicide and miticide.
I put two tablespoons of NEEM into a one gallon container, filled it with water and mixed well. I transferred some of this mixture into a quart spray bottle and went to work.
Working in small sections of the tree at a time, I saturated the affected areas with this solution and let it soak in for a few minutes, but did not let it dry on the leaves. Luckily I did this early in the morning while there was still good cloud cover. I gently washed each leaf (I really did...took me all morning!) with the NEEM and then rinsed the leaves off with clean water from a garden hose. I basically gave the tree a complete NEEM bath!
It was a lot of work but I got rid of most of the mold and the tree looks *so* much better. I'll likely have to spot treat it again soon but that's OK, I don't mind. My lemon tree is one of my favorite plants on my back patio and I don't want to lose it.