Everything I've read over the years leads me to believe that cannabis is probably fairly safe on the liver. If you have hepatitis C or some other form or chronic liver disease (which you don't if you've been put on Cymbalta), then you might have reason for concern if you were a heavy, chronic cannabis user. But if you have healthy liver function and are a moderate smoker, it's most likely that you're fine. Do a Google on "cannabis liver" and you can read some of the general information out there. There seems to be fairly good evidence that the active ingredients in cannabis (THC, for instance) can be downright beneficial for the liver, but it's important to note that that's true of isolated THC and not necessarily whole smoked cannabis.

The substances you should be a lot more wary of while using Cymbalta, which can cause some liver problems for some patients, would be alcohol and/or Tylenol/acetominophen. Definitely don't drink while you're using Cymbalta, and don't drink and take Tylenol at the same time, which is horrible for the liver.

Try and chill. Taking Cymbalta is probably much safer for you than being anxious and depressed. And combining it with moderate or light cannabis use is probably fine. If you want to be sure, get your liver function tested (simple blood work) while you're on that antidepressant and monitor your liver function while you're taking it. If you begin to show signs like jaundice or itching or elevated liver enzymes, you can change medicines and any potential liver damage should reverse itself. The liver is an amazing organ with incredible recuperative powers.