Is there such a thing as rechargeable lithium batteries?

Most non-rechargeable lithium batteries contain a sheet of elemental lithium metal. As the battery is discharged, the metal reacts to form lithium compounds.

Recharging such a battery is not possible, since the lithium won’t reform a uniform sheet again. When trying to charge a non-rechargeable lithum battery, lithium metal will reform, but not in the form of a flat sheet. Instead, it will form crystals which may puncture the separator and short out the battery. Deswegen, one should never attempt to recharge a non-rechargeable lithium battery.

Rechargeable lithium ion batteries don’t contain lithium metal, but chemical compounds which are rich in lithium. These compounds give off lithium ions when the battery is discharged, and during charging, the ions migrate back to restore the original compound.