I haven't heard or seen lying as a symptom or cause of depression. It seems that you are not happy with the job you are currently at and just made up an excuse that would work for future absences. By all means if you are not happy at your current place of employment than apply and actively look for another job. But in the mean time you should try to put forth some effort on the one your with now until you do find something new. You are only going to be short changing yourself by not doing your best and this is not going to help your depression or conscious.