No, just fill it up and use it.
There are two common types of rechargeable batteries of led rechargeable table lamps, one is nickel-metal hydride (cadmium), and the other is lead batteries.
The former has a memory effect, so when used, the electricity should be used up, and the electricity should be sufficient when charged, which can ensure the capacity of the battery; The latter is the opposite, when the LED has signs of darkening do not use it, need to charge immediately, nothing needs special attention when charging, but for a long time, the electrolyte will evaporate, so it should be added every few months.
If the charging lamp is used while charging, it will gradually reduce the charge storage of the rechargeable battery and may burn the original, and it is not necessarily burned as long as you use it like that, but it is risky. However, it will have a certain impact on the storage capacity of the rechargeable battery. If the lamp is used normally now, do not worry about it, and pay attention not to charge it next time