Just like with any creature, they all play an important part on lifespan.
A proper diet is indeed critical (feeding dog food is not acceptable), but they also need a proper temperatures to digest that food. A Savannah Monitor is incapable of proper digestion at low temperatures (under 100, I think I read somewhere). So, husbandry and diet play a vital part of lifespan.
Also having an obese Savannah will cut their lifespan dramatically. It is important to feed them a well balanced diet, and assure they are getting the proper exercise as well. A fat monitor is cute, but very unhealthy.