That's one of the few issues upon which libertarians, and even
Objectivists, have no specific stance. I've seen Friedman make
economic arguments against it, but I think in general libertarians
are split just as the public is.
I personally don't think the US Government, or any government on
Earth I've seen, has anywhere near sufficient moral integrity to
issue such a judgment, so I oppose it. Any government who would
knowingly execute an innocent man after using him to testify
against the real killer has no business being given that power.
(Jesse Dewayne Jacobs, by Texas in 1995. Governor George Bush Jr.
signed the death warrant.)
As far as punishing immortals, there's still isolation. Removing
one from public interaction and communication should be hardship
at any level of technology.