This is a sparkling affair. Libra is an air sign meaning that it lives in its fancy and it's a sense that life can be magic. Libra loves attention, loves to seek after something that's glamorous, something that is attention getting, as well as something that makes them feel pampered and as though they are being sought after and loved by the world. That basically is why a Libran is very social and why a Libran loves to get out into the world.
Sagittarius is also a sign of passion, passions of the mind and body. But basically, Sagittarius's passion is for freedom, for adventure, to lead a life that is spontaneous, that gives them a sense that the world is large, and they can leap almost anywhere they want.
So, the energies of both a Libran who is social and very oriented toward others and a Sagittarian - who is also oriented toward others because Sagittarius learns and experiences different cultures that way - work well. It may be for different reasons that they both love getting out into a wider world, but because they both do they both have a strong structure, in a sense.
Not that it's a structure in which they are imprisoned, but they have a strong center that can hold them. Basically, Libran loves being in a relationship. Libra is the sign of partnership, and Sagittarius loves having a partner in adventure.
Where things might break down a little has to do with more the mental aspects of this. As emotional partners, neither of them are particularly heavy in their emotions. But they do have sensitive and caring, and giving feelings. But in the thinking processes, what Sagittarius looks for is to be very free and independent and what Libra looks for is to have a partner.
So they may have to work out a little bit of, oh, let's say energies there about togetherness - how much togetherness is suffocating and how much togetherness is a companionship.