Seems like it may be faulty on/off switch contacts not staying in the operated position, when the switch is turned to the on position.
You may be able to replace the switch if a compatible switch i.e. same size and rating, can be found.
Post some images of the lamp showing the switch in your question. Here's how on ifixit Ajout d'images à une question existante.
If the lamp is new, check out the warranty documentation (user manual?) and if the lamp is still within the warranty period, (check the date on the purchase receipt to be sure) contact the manufacturer's customer service section (or the place of purchase) and make a claim for a replacement or a refund.
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