No, it really isn't. At least it probably isn't.
It is fairly well accepted, based on a number of studies, that the death penalty is the most expensive option. Of course, there are some who dispute the findings of these studies and argue the death penalty is slightly more cost effective, or could be with some reform of the process (fewer appeal options, etc). As I have not been able to do a thorough examination of the studies and data, I can't comment on the findings. But for the record, the studies include the cost of internment and not just the cost of the legal process.
But let's say for a moment the studies are wrong and it is a bit less expensive to put a prisoner to death than to inter them for the remainder of their life. Is that really the way to decide which is the right punishment to implement?
More troubling, to me at least, are those who want to make the death penalty procedure less expensive by limiting the number of appeals (among other things). Hell, let's just eliminate the trial! That will save a bunch of $$.