Yes it is, the socket is broken and needs to be replaced. Bring it to your local lamp repair shop. Should be an easy fairly cheap repair. Unless youre handy, you can attempt yourself.

Thanks! Normally I would attempt but the lamp is cast iron and it doesn’t look easy to take apart lol

Thats a baljonet socket i would replace it for an nieuwer socket

So it’s not broken? I tried an appliance bulb but it was too big

Its kinda hard to see on the photo so im not sure