I've lied to get out of things many times. I like because of many reasons but mostly because I have severe guilt regarding the "why". Having anxiety or any other mental health condition is always understood by others. Alot of times I myself can't help but ask "why can't I just be normal and do this". Regarding your work situation, you know in your heart if you can do this project without a breakdown and if you know you can do it, then do it!! If you know it's beyond your mental ability to handle it say no and depending on your relationship with your boss the answer could be, it's not a good time for me to take on this task but thanks for the opportunity, please consider me again on the next time or if your boss knows about your anxiety them you could be more specific. I would just try to think about longevity in your career. Good luck!!