Gravity on Moon is less as compared to gravity on Earth.. But it exists.
It is possible that water, air, atmosphere etc. on the surface of moon and around it, had escaped from Moon because of low gravity. The rotation of Moon about itself has probably helped the air, water and atmosphere from surface of Moon. Also, the temperature range is quite different on Moon than on Earth and is unsuitable for our sort of life.
Water, and oxygen are required for survival of life like the life found on Earth.
But perhaps there is some other type of life which does not require water and oxygen but requires some other things and can survive in the conditions on Moon. We do not know about it.