Is it possible for a lack of exercise cause a woman's menstral cycle to be absent or erratic?

Not necessarily. Although if there is significant weight gain or signs of excessive hair growth in unwanted areas, you may be developing pcos which is known to affect menstrual irregularity. Because of your age, I dont think your close to menopausal age (average age in the us around 51). Have your self checked by an endocrinologist (make sure your thyroid levels get checked). Good luck.