Could it be healthy to train for a half marathon with a sprained ligament in the knee?

You will run . The risk of further damage, irritation, even rupture if is not healed enough. If it causes pain, listen to your body and give it a break. If there is no pain and you feel like you have healed enough, consider slowly starting back, paying close attention. Discuss with the physician who diagnosed the sprain prior to moving on. Best of luck!