Is the gym responsible for lost item/stolen item?

The gym is responsible only to the extent that it represents that your belongings are safe. I myself belong to a gym and leave belongings in the locker room when i work out.  The lockers in the gym have the ability to have locks put on them.  In other words, most members bring their own locks and lock their locker while they work out and remove the lock when they leave so another person canuse the locker.  If the lockers at your gym do not have the ability to lock, you may have a good case, however, by you leaving your belongings unattended, you risk that someone will take them.  usually, gyms have warning signs in the locker room warning you about this.  I do not think that you will be able to sue the gym if there is a way to lock the locker.  Isuggest that you make an insurance claim if you can if you have insurance on your cell phone.  In the future, leave your wallet in the car and your cell phone.