You are more likely to find lichens on unhealthy trees, but lichens are not the cause of the trees' deterioration. Lichens are related to mold and moss and grow well on trees suffering from other issues, because the plants are not healthy enough to fight them off. Lichens do little damage other than blocking some sunlight from getting to the tree, but you can remove them for aesthetic reasons.
Start by getting as much of the lichen off of your tree as you can. Fill a bucket with warm water, and add a few drops of liquid dish soap. Grab a stiff-bristle scrub brush, and scrub away at the bark of the tree to get the lichens off. Don't use any chemicals other than the dish soap, and don't use high-pressure cleaners, such as a power washer. These other tools and materials will harm the tree just as much as the lichens. A good scrubbing will remove many of the lichens clinging to your tree, giving you a chance to prevent them from coming back.
If scrubbing doesn't seem to work, a sure-fire way to kill lichens is to cut off their exposure to the sun. Lichens like to gather on trees because that's where they can get the best exposure to sunlight in order to grow and thrive. Covering the lichens with shade cloth will choke out their exposure to the sun and gradually kill the organisms. However, this will also block out sunlight to at least part of your tree as well, so this procedure should only be used if you know that the tree is in serious trouble and you have a plan for recovery or replacement.
No known herbicides or chemical treatments kill lichens. Your only other option to remove these mosses is to improve air circulation throughout the tree. Trim away branches heavily covered in lichens, as well as any excessive foliage. Remove branches that are closely crowded or rub together, as these allow little air circulation; such stagnant air promotes lichen growth. Most trees benefit from pruning every year or two in the spring to remove damaged or dead growth anyway, and this practice will help to prevent lichen growth.
The most important and effective treatment of lichens is to keep your tree as healthy as possible. Along with regular pruning, this involves following and maintaining the proper watering, feeding, mulching and harvesting practices for your particular species of tree. Stronger trees will not attract lichens. Improving the fertility of the soil can help the tree develop a fuller canopy, leaving little room for lichens to move in. If you are unsure about care for your particular tree, consult a professional landscaper or someone from a garden center, nursery or extension service for help.