Should people who are sentenced to life in prison be allowed the death penalty as an option, and why?
Well, this is totally moot in countries that do not have a death penalty on the statute books, like the UK.
As a side-topic, though, yes this should be allowed and it should be allowed for someone to ask for euthanasia be it for reasons of mental health, health or just can't be arsed to live any more. Yes, there should be red-tape and hoop-la that they would have to leap through but there should be a means for this in our country. Lets face it, we treat our pets better than we treat our relatives and selves.