A Lunar Atmosphere
My Tool
I wrote an atmosphere calculator based upon thermal (Jean’s Escape) with empirical fudge factors to increase the rates of atmospheric loss to more along the lines of what we see in the Solar System. It correctly predicts an $N_2$ atmosphere for Titan and no atmosphere for the moons of Jupiter.
What I see
This calculator shows the half-life of water as ~$2 \cdot 10^5$ years in a lunar atmosphere. It gives the half-life for $O_2$ & $N_2$ as ~$10^6$ years.
Some Assumptions
Human Time Scales
Assume a human generation equals 20 years. We would only lose ½ of the water in the atmosphere in 200,000 years – meaning a non-technological society could survive at least 10,000 human generations (i.e. 1 atmospheric half-life for $H_2O$) without replenishing the lunar atmosphere.
Lunar Atmosphere
The Moon’s gravity is ~1/6 of Terrestrial gravity. Atmospheric pressure is generated as the weight (mass * gravity) of the column of air above the measurement point. So to maintain the Terrestrial atmospheric pressure at the Lunar surface, we need 6* the mass of gasses above the observation point.
The surface area of the moon is 7.5% of the Earth’s. When you multiple 6x the column of atmosphere * 7.5% of the surface area – we get 45% of the Earth’s atmospheric mass. 45% of the Earth’s atmospheric mass comes to $2.35 \cdot 10^{18} kg$ ($2.35 \cdot 10^{15}$ tonnes) of volatiles in the correct combination.
For the atmosphere we will need:
- $N_2$ - $1.8 \cdot 10^{18} kg$
- $O_2$ - $0.5 \cdot 10^{18} kg$
- $H_2O$ - $0.2 \cdot 10^{18} kg$
- Subtotal - $2.5 \cdot 10^{18} kg$
Hydrosphere
We will need excess water for standing bodies of water and icecaps. I will estimate the liquid water requirement by scaling Moon / Earth ocean mass to the ratio of Moon / Earth surface area.
- $H_2O$ - $1.05 \cdot 10^{20} kg$
- Total - $1.07 \cdot 10^{20} kg$ (atmosphere + ocean)
Let’s assume our gases do not react with the surface of the Moon (probably a bad assumption but it makes life easier, so I'm going with it) so we don’t need to juggle those numbers based upon probable chemical reactions.
Obstacles
Finding the water and oxygen in our Solar System would impose no problems. However, finding this amount of N2 might be difficult.
Saturn's moon Enceladus (about 240 km diameter and $1.08 \cdot 10^{20} kg$ of mostly water mass) would provide the necessary mass. However, it would not have the correct ratio of elements. We'd probably have to scale up to a slightly larger moon and "crack" a bunch of water to release $O_2$ into the air. We could use the $H_2$ as propellant for moving Enceladus (or its replacement) so it collided with the Luna. I have no idea what it's $N_2$ content would be but would expect it to be deficient.
What would it would look like
Scale height of a Lunar atmosphere (assume same temperatures as Earth’s) would be 6x the 3.7 mile scale height of Earth's atmosphere. Meaning that it would be over 22.2 mile scale height. No one would have trouble breathing on any Lunar mountains.

Most of the land would be on the so called "Dark Side" of the Moon facing away from Earth. Most of the region facing Earth would be a giant ocean.
Neat stuff
Flying
Given this atmosphere density and Lunar gravity, people should have no problems flying by putting on some specially crafted wing sleeves and flapping their arms.
Imagine mansions situated on Lunar peaks. Physically fit people would visit their neighbors by putting on their wings and flying to the next peak over.
Walking on Water
People could run across bodies of water without falling into them (surface tension could hold them up).
Radiation Protection
Despite the lack of a strong magnetic field, this idea has the added benefit of providing plenty of radiation protection. The added mass of air (6x that of Earth) means that colonists are well protected from radiation.