Here's another Tarot card for Libra: the 2 of Swords.
This card corresponds to the Moon in Libra. Its title is "Peace Restored." This perfectly expresses the needs of a Libra Moon.
This is a quiet card. It can indicate staying silent to keep the peace. There's a choice to be made when you see this card, but you're not ready. You'll have to decide eventually, so it's only temporary.
This card can also represent the refusal to make a choice, because everything seems like a good idea (or nothing seems like a good idea). When reversed, it's a warning to think carefully before you make a choice (you're in danger of making an unwise, impulsive decision).
Most versions of the 2 of Swords show the sword wielder wearing a blindfold (as in this version from the Tarot of the Magical Forest deck). It can mean shutting your eyes to a truth, or shutting out the world in order to find peace. Sometimes this card shows up in a "love is blind" scenario.
Moon in Libra needs emotional equilibrium, and often tips back and forth in order to maintain it. Hence this Moon's rep for being fickle or moody. Really, it's just inner adjustment, with the goal of finding that still, silent moment.