What is the likelihood of being able to lift weights and play sports after having surgery for thoracic outlet syndrome?

Wait and see: Likelihood data will not matter at all. What will matter is doing the best you can to heal as optimally as possible and to find expert coaching willing to collaborate w/ Drs to take it step by step as far as it can safely go. Even a high % w/o such a plan won't work and a low one might rob you of hope. Just "Do the right things" and see how far you get. Best wishes.