Planet Found in Habitable Zone Around Nearest Star

[Anomalocaris]

Hence the need for a solution other than a straight line rail of a laser.

The laser propelled spacecraft needn't travel in a straight line.  If it's light sail is reflective it can angle the light sail to get off axis thrust.  It has considerable room to maneuver laterally and alter its own vector without resorting to chemical thrusters.  It just need to be able to signal its location and maneuvers to earth so the laser tracks it and not lose it as it maneuvers.