I know it’s the old round pin we used for phones back in the day but can someone send me a link to the exact one because I’m seeing too many round pin charges of different sizes. Also where do I go for tech help related questions like these? Is this the right community?
As it has been mentioned, it's a barrel plug, but there are dozens of barrel plugs of different sizes, some even have the same outer size but the receptacles for the central pin have different diameters.
Check the polarity and voltage, and try to measure the diameters if you're buying online.
If you're buying locally, take the lamp with you and ask for advice to the seller.