How long a battery operated lamp lasts varies based on various factors.
The battery may last for anywhere between a couple of hours to more than 40 hours before requiring a recharge (for rechargeable batteries) or replacement (for non-rechargeable batteries). This depends on the battery type as well as the lamp’s brightness setting during use. Rechargeable batteries will last for about three years but even this will vary depending on frequency of charge/recharge cycles.
The lamp’s LED bulb could run for thousands of hours. The lamp itself may work for years depending on frequency of use and the quality of handling.