I learned something in this thread, that red was for "hostile" and blue for "ally".
That said, I got to echo (and add stuff to) some of kmunoz's remarks.
I think the lines should just reflect the colors of who controls neighbour nodes, and either some icon (like shield in the middle of the lane for ally, sword for enemy) or changes to the line pattern (like broken in the middile, dotted, zig zag, or whatever, and so on) should represent hostility. Or, maybe it would be possible (and not ugly) to make the border of the lane reflect hostility (red sides if hostile, blue sides if ally, or something like this). Or make it pulse from its color to another color to make hostility. It looks like hours of tests to make it clear to the player though. Sorry.
The number of factions in a game can be high rather fast and, to be honest, I'd just like to be able to play as "red". I'd prefer if lane colors just represented faction ownership, and nothing else.