Should prisoners with full life sentences be given the chance to end their life rather than live out their days locked up?

In an ideal world, yes. The goal of the justice system is to deter certain behavior and prevent repetition if it happens anyway, preferably by rehabilitation or by keeping someone out of society if that's not possible. Punishment can be a means towards that, but isn't a goal in itself. Both lifetime in prison and death accomplish the separation, and a choice would be the most humane offer.

That said, I don't trust the system enough to rule out coercion, so in the world we live in, my answer would be no.