Obstacle avoidance is not perfect. We cannot guarantee, and neither can DJI that it's going to work in any given scenario. It's much more likely to see a wall than a crane, cable or even bare tree.
Personally I would avoid flying where there is a risk of hitting a tower crane / light towers. OR plan separate flights to give the crane a wide berth.
However, ways you can increase confidence:
1) Fly slowly. We limit flight speed automatically when OA is enabled, but you can reduce the speed of flight on waypoint missions using the right hand thumb stick (down for slower, far down for reverse). You can also reduce the max flight speed overall.
2) Test it first - fly manually up to the object and test the sensors in DJI Go. They give visual feedback on what's being sensed by the obstacle sensors.
Overall, light towers sound very difficult for the sensors to spot, and I would not expect obstacle avoidance to reliably sense and avoid them.