If capital punishment worked, people wouldn't murder people in the USA where the death penalty exists.
It doesn't work, it's not a deterant to this crime.
Life sentences are life. They serve a custodial tariff and then they are released on license till they die if the parole board allow it. All under MAPPA with probation, and PPU managing them. They have exclusion zones and disclosures are made about them to any landlord or employer.
It's cheaper for the tax payer to have them on UC and managed in the community than pay for them to be in prison for life. They don't really get a life anyway. They are watched till the day they die, the only difference is they tend to be in a local authority flat on UC all day than in a cell.
I've known lifers deliberately breach their license such as shoplifting to just go back in, because it's easier. You also don't get many who murder and then go on to murder again in the UK, because the rehabilitation of lifers in prison is good for murder. A lot of money goes in to it, they engage with their OM courses. If they don't they don't ge parole, so then would spend life in prison.