What should you do with a worn-out Li-on battery?
Are these not rechargeable?
If it's not rechargeable (i.e it's too old and too well used to retain a charge), you could take them to a recycling centre for disposal. You might have to pay a fee if you have half a tonne, but a recycling centre should have methods of safe disposal. Failing that, you could (nicely) ask the chemistry technician at your high school/university. They are likely to help you.
ETA: Our local supermarket has a receptacle for used batteries. When waste is sorted at the source (rather than the destination!), it makes recycling measures much more feasible and economic.