My question is: I have only 1 muscle on my left arm (one of the biceps muscles is completely gone. A unicep if you will). Should i train that arm with lighter weight? Being that it is 1 muscle short.

Thats a good question and one I have never had asked. My suggestion would be if you have a doctor to consult with him/her first. As in relation to muscle, as long as you can train and execute movements similar with that arm, then go ahead. Muscle is muscle and responds the same and will grow when a stress is applied. Go for weight that still allows you to push yourself. Vary the weight one week with light weight and high reps, and then the other week with heavier weight as long as you do not push too hard in which will injure you. Once again these are suggestions and you really should find out from your doctor first as they would know best in your situation. One thing you might want to try is rather than using free weight, try the bands.