Lunesta contains eszopiclone which is an nonbenzodiazepine and is used to treat sleep disturbances. This drug is not tested in drug test. This drug has a half life of 6 hours and no drug is available after 24 hours. Even if you are tested positive for this drug then a valid prescription from a doctor can protect you.
To the best of my knowledge, there is no routine test for detecting Lunesta (although most drugs can br detected by GS/MS if one knows to look for them specifically). I have heard of false positives for benzos being attributed to lunesta use but I think that is speculative and not substantiated by medical evidence.
Any 'drug' is going to show in tests
No lunesta is not a narcotic , don't worry about it I might add your Dr passed on to you a crumby drug he F** ed you it does not even work oh maybe if you are a baby but still just the same it's not a narcotic don't freak on it .