Personally, I think it sounds like maybe this would be a good opportunity for you to stretch out of your comfort zone, you may surprise yourself with what you're capable of. But, your mental health is as good a reason as any to say no to something. If lying will cause you to feel bad about yourself, just be honest about why you don't want to do it. I know a lot of people try to hide mental health concerns from their employer but I work in human resources and I see a lot of problems that could have been avoided with some honesty - if they know you have issues they need to be aware of and work around, they will be less likely to put pressure on you to cross those boundaries.