Slower than light or faster than light?
If you invoke some kind of magical FTL, then the nuances of that FTL will determine everything, and they can be tweaked to produce any results that you desire.
However, for relativistic slower-than-light interstellar planet that fits physics as we currently know it (e.g. engines spending limited fuel/energy to accelerate, and as much energy to decelerate), shipping lanes don't really make sense because:
* You don't stop in the middle as a trip with an intermediate stop takes exactly twice as much fuel and significantly more time as a trip without a stop;
* Interaction requires matching speed, not only position - if you're not willing to spend fuel to make an intercept, then you either fly past each other at ludicrous speed or get destroyed in a collision;
* Direct routes make practical sense - on land, you may want to follow roads and go through major towns on the way, so route from A to B will have travelers passing from C to D through A and B; in space the optimal route is a straight line between C and D without detours.
* the lane would be empty. Even if some ship would be destroyed en route, it would simply fly further with the same speed forever until it flies past (or into) the destination.
* as everything moves relative to each other, two ships going from A to B at different times will take different routes. Assuming slower-than-light travel times (years between stars, days or more between planets), if a faster ship leaves after a slower one, it may reach the destination before the slower one but it will never "meet" it, since they travel on different paths unless it intentionally went on an intercept trajectory and not to the destination.
Realistic physics don't really have unplanned encounters
Engines that can get you from Earth to Jupiter in weeks or from Earth to another planet in less than millenia are visible from far, far away, and also give up your exact location, direction and speed - i.e., source and destination. Any maneuvers require firing the engine - want to start moving? Throw out lots of matter or energy into space. 947
Want to stop or steer? Same thing. Want to move with speeds that get you anywhere soon (as opposed to going from earth to a comet in 10 years) - throw out lots of energy once. I recall seeing calculations that if such a ship was moving between planets in Alpha Centauri, then we'd be able to track it with our current technology from Earth.
So no encounters can be really unplanned - a ship would know all the ships in the neighbourhood, and observe all their maneuvers long before they have any effect - i.e., if someone is changing their speed to meet with you, then you know that they have done that long before they actually meet with you. Before you launch, you'd have a database listing where exactly every ship currently is moving, even if they were launched decades ago. Furthermore, everyone else knows if any meetings occur, and where they go afterwards - if a ship gets intercepted, then everyone in multiple star systems know that and also know where both ships go afterwards. 199