Could ice exist in Lunar lava tubes?

[Al_]

http://en.wikipedia.org/wiki/Lunar_lava_tube
Given that they are expected to be at about -20C and parts of them will be in permanent darkness. If ice can exist at the Lunar poles: http://nssdc.gsfc.nasa.gov/planetary/ice/ice_moon.html
then why not there?
If water molecules migrate from the equator to the poles http://www.lpi.usra.edu/meetings/lpsc2012/pdf/1110.pdf will they become trapped in such caves?

 

[Al_]

Doh!
I did a bit of research and answered my own question. No is the answer.
http://www.quora.com/Does-ice-evaporate-in-a-vacuum
Basically, it would have to have a constant steady input of water vapour (basically a thin atmosphere), or much colder temperatures.

 

[stefan r]

My impression was that the water found on the moon was adsorbed in the regolith. On earth, clay retains water molecules at higher temperatures.

The basin at the south pole might have lava tubes. The inside of tubes on the poles should be colder than tubes at the equator.

Honestly I do not know what is on the surface of a lunar lava tube. It must have a surface. Would be nice to have a sample.