Here at SED Optical Eyecare, we would recommend that you do not carry lime around in plastic bags. As the sun heats up the plastic bag, the lime will expand, which can cause the plastic bag to explode.
Additionally, if the injury is poorly managed initially, it can cause severe sight impairment that can be hard to treat and may require surgery. If you ever get lime in your eyes, you must wash your eye out with copious amounts of water and then immediately come to see us. This is only way to ensure that the lime has been fully flushed out of your eyes.