Let's take a 15-20 year case example in the People's Republic of Kalifornia...
If a gey gets LWOP, then he will probably go general population, in a mid-level prison. Until he screws up or becomes a he-she. Then he might need more supervision.
And at the end of 20 years he will still be alive.
If a guy gets Death, he will go to "condemned row" on San Quentin. He will be in isolation, and the officer/inmate ratio is much higher ($). The state will hire him a team of high-priced defense attorneys (NOT public defenders) who specialize in death penalty cases. The billing department of said team knows that the shitbag is not paying, the taxpayers are. So the bills reflect the deep pockets of the state treasury. Multiply that by all of the times the case appears in court (clerks, judges, DAs, police overtime, court operations personnel, etc...).
And at the end of 20 years he will still be alive.
Trust me, I agree with the .30-06 example above, but in reality it costs A LOT MORE for the death penalty than for life without parole.