Wilting and black spots on your lavender plant may indicate that your lavender has root rot. This condition occurs when the soil is too moist to grow lavender properly. Instead, a fungus begins to grow on the plant, slowly causing it to die.
A lavender plant with black spots on its leaves or brown or black discolorations on its stem may have a plant disease called shab. This disease spreads easily from plant to plant -- especially if your lavender plants are planted closely together.
Help to halt the spread of shab by pulling out the infected lavender plant by the root with gloved hands. Burn the plant, safely, do not dispose of the plant in a compost pile.
If you notice the signs of root rot, then cut away the infected parts of your lavender plant. Plant new lavender plants in soil that is well-drained. Lavender plants prefer soil that is moist, but not over-watered. Soil should not have standing water and should receive at least partial sunlight. This encourages growth, while drying the soil.