Yes, it is possible that the eye color of adults can change, and it can also only happen to one eye. It is then called Heterochromia. There are two possibilities for different colored eyes, either congenitial (genetic) or acquired. Since you ask only for eye color changes in adults, we can skip here the genetic reasons, as these show up in kids already. If you are interested in them, have a look into the Wikipedia article on Heterochromia.The basis for our eye color is genetically determined, changes can later occur due to diseases (so if one experiences a change in eye color, it is always a good idea to consult a doctor) and also due to medications.The eye undergoing a change in pigmentation can either lighten up or darken.
No. I think. As far as I know/understand, you are born with the genetic code that dictates what eye color you will express. It's understood that some babies change eye color as they develop. You can think of the body "switching" on certain genes, that influence eye color, to retain more pigment. That's why eye color will become darker, not lighter during development. This is how it works naturally.