Q.what is causing my lime tree leaves to turn black
Some leaves are getting blackish or molding.
Certified GKH Gardening Expert
It's called sooty mold and is common on citrus trees. While unsightly, it's usually harmless. The mold grows on the sweet honeydew from sap-sucking insects like aphids, scale bugs, etc. You'll first need to treat the offending insect pest (hosing off plant and using garlic spray, insecticidal soap, or horticultural oil). We prefer neem oil, which is safe and effective. As a bonus, neem oil also make a great fungicide, so it will usually take care of both issues.
Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm