Maybe I overlooked it in the rulebook, but I was wondering if it was at all possible to play LS v LS or DS v DS and if so what were the victory conditions in those matches?

Nothing in the book, and I imagine the way the factions are designed, they're not really built to compete against each other. Doesn't make much thematic sense either (although you could make an argument for Sith vs. Imperial Navy). But I suppose you could just copy the victory conditions of whatever sides are playing.