I don't think biomimicry is a panacea to all the problems we face. The premise of biomimicry is that we can learn from nature and adapt solutions to solve our problems in a sustainable way just like nature without waste. This is an idealistic approach. Having said that, yes nature does handle many of these issues. I don't know about lunch cancer but many organisms in nature have self-healing ability which may provide some directions for you to research this topic. Also, check the website, asknature.org and this site is hosted by biomimicry Institute.