The only way to combat moss is to change the environment by tree removal and/or pruning to allow more sunlight and airflow. This should be coupled with physical removal of moss prior to aeration and seeding in the fall to establish a better stand of turf in the area. Another option is landscaping mossy areas as an alternative to grass.
Mosses are non-vascular, absorbing water and nutrients mainly through their leaves. They are typically found in moist, shaded areas with poor air flow. Lacking seeds and flowers, mosses reproduce via spores. While mosses can tolerate a wider pH range than grasses, the presence of moss does not always indicate a low pH (acidic soil). To accurately gauge the pH of the soil, a soil test is required. Lime neither prevents nor remedies moss.