Does nikon camera goes with a vivital lens?

I have a nikon D2x and want to buy ar Vivitar Macro Focusing Zoom 52mmLense
Whould they work together?

Consult the User Guide.

The D2x has an APS-C sensor, so if you buy the Vivitar lens with a Nikon mount, it should work. As for focus and aperture control, the lens write up should tell you.

Vivitar put their badges on some rather nice lenses back in the days of MF, but I wouldn't trust their current output.

MF lenses have problems on AF Nikons anyway, so I'd be careful

If it's a Nikon mount version, then it should work.

But seriously - you have a pro grade D2x and want to put a $30 lens on it? Ugh… That'd be such a waste of your fine camera! The quality of the lens is absolutely essential for good image quality!

I'm not aware of any 52mm lens, perhaps that's the filter thread size? There's a 70-210mm one and a 75-205mm one

The person selling this on eBay don't even know what they have.

The pictured lens is actually a 70-210 mm zoom (manual focus) and the only thing about it that is 52 mm is the filter thread.

Your not seeing this, makes me wonder how much experience you have using various lenses on your amazing (but old) Nikon D2x and what the various terms mean when describing lenses and cameras

It is usually a good idea NOT to buy photographic equipment from someone who does not know what they are selling. At least that lens has a filter on it, so the chances are the front element is in pretty good shape. What problem you will encounter is that the lens is not specified as having a Nikon mount. If it did, for you to use it on your fine camera, you would need to have it converted to an AI type mount or you can't use your cameras meter

You need to ask the seller some more questions