It is wise to avoid the use of lime in compost piles. The addition of lime will increase the pH* of the compost pile and convert ammonium nitrogen to ammonia gas, which leads to the loss of nitrogen. Without the proper level of nitrogen available, the microbes responsible for decomposition will not function effectively. Finished compost is usually slightly alkaline without the addition of lime. Knowing the pH of your soil (acidic or alkaline) is important as well. For example, you would want to avoid high pH materials or compost if your soil is already high in pH or alkaline.
*pH is the measure of how acidic (sour) or alkaline (sweet) something is. The scale ranges from 1 to 14 with neutral being 7. The lower the number, the more acidic. The higher the number, the more alkaline. Sulfur is often used to make soil more acidic, while lime is used to make it more alkaline.