Does carnitine liquid work for weight loss if you do lots of sports?

Possibly. There are not really a lot of good scientific studies but understanding how it works, when exercising and taking in a low to moderate amount of carbohydrate there have been reports of enhanced weight loss with liquid carnitine.
Improves weight loss. Study done - one group was given 2000 mg of carnitine, and the other a placebo. In the placebo group, the average weight loss after 12 weeks was one pound. In the carnitine group, weight loss averaged 11 pounds. That’s an eleven-fold increase in weight loss, simply by increasing carnitine levels.