The things we value most often serve as an extension of our self-awareness. A favorite hat, car, or relationship reflects a part of how we feel about ourselves. Therefore, the loss of such an object in a dream is significant. It is equally significant whether you actually own the object in waking or not.
If the thing lost is an inanimate object, what does it symbolize for you? Examples would be jewelry, favored clothes, or pictures and family heirlooms. In losses of this kind, the indication may be that you are nervous about losing an expensive or important new object in your life.
If a person is lost, the first question to ask is, "Who?" It may be that you have questions about your commitment to another or their commitment to you. However, it is not to unusual to be looking for a stranger.
Why are you searching for this person?
Do you find this person? Where?