And if you need to flip lines, there is a tool for that, or you can do in an edit session manually.
Flip Line—Help | ArcGIS for Desktop
Flipping the direction of a line—Help | ArcGIS for Desktop
Use case example (but not for routes), I use the flip line in a script whee I need to buffer a flight lines, based on the value in a field (left or right). Originally the lines are all contiguous and "in the same direction". I select all those with the on field = "right", flip them, then I can buffer them using the left option and they will buffer as I need them. I mention this to point out that it can be scripted if you have some way to select those lines that are "in the wrong direction".