Your idea sounds generally right.
If I understand the use case correctly, your model is already able to predict the lanes, but cannot output each lane separately?
If that’s the case, would a post-processing step be OK for your use case or does it violate the benchmark evaluation?
You could e.g. use OpenCV to detect all lanes via a connected components analysis and add a tag to each line.
If that’s not possible, you could use a multi-label approach with 6 classes.
For this use case, your target should contain 6 channels, where each channel would be a “class” (in your case a lane), containing 1s for the current line.
I’m not sure how well this multi-label classification approach would work for the same object, but might be easy to try out using your current model and training.