Does lack of atmosphere on the moon make earth-shine more, or less, bright? The earth acts like a light-globe in the sky for half of the moon, the side that is facing the earth. In what way does lack of moon atmosphere influence earth-shine. Does it make earth-albedo brighter, or dimmer? Either way, do we know with how much? Put differently; would an atmosphere make it easier, or more difficult, to read a newspaper on the earth facing lunar surface, after sunset?
The lack of a lunar atmosphere doesn't affect Earth's albedo at all, since albedo is only a measure of the diffuse reflection of a body.
However, the apparent brightness of the Earth as viewed from the surface of the Moon would be affected if the Moon had an atmosphere.  This, of course, would depend on the atmospheric composition of the Moon.
If the atmospheric composition of the Moon was such that it absorbed visible light, then the Earth would appear dimmer, or perhaps not even be directly visible (similar to how we can't directly see the Moon when the weather is cloudy here on Earth).
If the atmospheric composition of the Moon absorbed almost no visible light, and was highly refractive, the Earth-Shine might be overall brighter than if the Moon had no atmosphere at all. The refraction would bend some of the Earth-Shine into the surface of the Moon which otherwise would have passed by. This picture shows the analogous situation for Earth and the Sun: