While women feel unsafe as a general rule, there's no reason to make them any more unsafe (or feel unsafe) than they already are.
I think in the case of countries where this has been a common practice, killing the perp would result in a paradigm shift about what's at stake when you strike out to maliciously wound a woman. Crimes without severe punishment don't seem as severe when there is nothing at stake for the perp. I also admit there are other things that would help - such as make it a hell of a lot harder to buy sulfuric acid, and teach children about respect for women and conflict resolution skills at an early age.
There is no such thing as a sentence to life in solitary. Solitary is something you get once you are on the inside and you somehow screw up while you are in there. It's definitely highly debatable whether putting certain people in prison in life is even that much of a punishment - Manson was unhappy to get out prison and happy to go back in. Jack Henry Abbott was a creature of prison and should have never been let out in the first place. I don't think they are suffering by going back in to prison for life. But the members of Tate's family sure are suffering.
With respect to vengeance or retributive justice. Personally, I believe in restorative justice for a lot of crimes - where someone else's life was not taken, or incredible cruelty was not exhibited. If you violently rape a child or wantonly take someone's life, however, there is no way of squaring or making good the offense. I believe most murders merit no more than a life sentence. Serial killers, child killers, spree killers, or sadists deserve death. I think it's cruel and perverse and sadistic for society to continue to shelter, clothe and feed people who have committed those crimes.