By how much?
I doubt anyone can tell you exactly. Not even a lamp manufacturer, until a series of lifetime tests were run, which is very time-consuming (obviously) and expensive.
Generally, physical/chemical processes that limit the lamp lifetime, arctube corrosion, sodium migration, electrode sputtering and so, should follow Arrhenius law, meaning that decreasing of the temperature will slow down them. But, decreasing vapor pressure will promote sputtering. Also, decreasing electrode temperature will decrease electron emission, and in the end, increase cathode drop, ion bombardment, and finally, sputtering.
Lifetime vs power curve is well-known for simple tungsten incandescents, but things are much more complicated in discharge lamps.