If someone lived on the moon how long could they survive on it?

That depends on a number of veriable factors including: What kind of life support system is in place, is Earth resupplying the lunar base with food, water, air and fuel, is it just the one person or are there more people in the base, and what kind of radiation sheilding is the base equiped with.

Under ideal conditions, with Earth resupplying the base, one could survive on the moon just as long as someone could survive on earth. Without any support, and without shelter, air, heat, water, food, and medical supplies, (in order of importance) one would only last anywhere from a matter of minutes to a matter of weeks or months.