Apparently, the hypnopaedia conditioning was not 100% effective with Lenina. She enjoys being with just one man, and there is some atavistic magnetism from the moon that she senses. In the real, natural world, the tides are moved by the moon, and animal behavior is affected by full moons. During full moons, fish tend to be more active, as well, and often breed at this time.
It is significant that Lenina senses, perhaps, the energy from the moon. Certainly, there is something primal in her nature that wants to respond to it. However, she is not quite capable of genuine, whole feelings because her conditioning tells her to reject it. All Lenina experiences are twinges from a soul long buried in conditioning, consumerism and soma.
The intuitive John, who loves nature, senses the inclinations that Lenina has towards it and assumes that she has some natural feelings. But, such is not the case. For, Lenina is simply not capable of feeling as John wishes her.
There are at least three places in the book where Lenina either looks at the moon or remembers looking at the moon.
The first is in Chapter 5 where she remembers a time when she was a child and woke up in moonlight. This was the first time that she ever noticed the hypnopaedic conditioning tapes going.
The second time is in Chapter 6 when she is out flying with Bernard and does not like the way the moon looks as they fly along on the cloudy night.
The third is in Chapter 12 where she looks at the moon for a moment before going off with the Arch-Songster.
I think that in general the moon is a symbol of the natural world for Lenina. It represents things that are not part of the utopian society. I think that is why she hates it so much in Chapter 6 -- she dislikes the fact that it looks natural and not controlled.
I think that she sees it differently in Chapter 12. She is attracted to the savage and, somewhat, to unorthodox behavior now. So she lingers, looking at the moon, instead of going with the Arch-Songster (probably off to his place to sleep with him) like society says she should.