This may be due to Anthracnose
Anthracnose, sometimes called leaf blight, is a disease mostly affecting older or weakened lemon trees. It is a fungus that generally begins on a dead branch and spreads to healthy ones during rain. Symptoms include browning or curling leaves, premature leaf drop, twig dieback and dark stains on the fruit. It occurs more commonly during wet and long spring seasons. You can prevent it by keeping the area around the tree clean. As a fungus, anthracnose will grow in leaf piles and wet, warm conditions. Rake well under your tree and prune dead branches as soon as possible. Once an infection has occurred, it can be treated with a sulfur or copper-based fungicide but you can't cure it.