Bulk of the expense for execution comes from the high cost of the mandatory appeals process, which often takes decades to run it's course. Texas usually manages to expedite the process more than most states, but recent rulings by the higher courts regarding guidelines for appeals have slowed their adjudication to roughly the same rate as other states. Second, the cost of defending the legality of using capital punishment in state and federal courts is figured into the overall expense of executing prisoners in most studies thus far. In addition, "death-row" incarceration is expensive as well, as they are separated from the general population for the time their appeals processes run. The studies mentioned above have shown that the overall cost to the state is higher for completed executions than the average expense to incarcerate for life, but there are detractors who dispute the methodology of the studies, and cost varies widely from case to case.
My synopsis of several articles I've read over the years when I first doubted the validity of these claims.