Diseases arise due to three factors occurring simultaneously. A susceptible host (stressed lawn), a pathogen capable of infecting the host, and the environmental condition that favors the development of the disease. In the plant world this is affectionately called the disease triangle.
When a lawn gets mowed too low, a stressor is created by damaging the plant. That damaged site often times is the way in which a disease enters the turf. Most pathogens that infect turfgrass are caused by fungi. Most fungi live in the soil in a dormant state, until the environmental conditions are present for their growth.
The environment is the hardest to predict and impossible to prevent. Some disease require cold and wet conditions to exist, while others need hot, humid conditions. When certain conditions exist, its important to manage the water, the mowing, and the fertilizing to reduce the possibility for an occurrence. Additional steps like planting disease resistant grasses, or applying fungicides can help to control a disease outbreak.