Does my lenovo t520 have a dvd/cd burner on it?

Look on the side of it, do you see a DVD/CD burner?

By default the drive is a DVD player and a CDRW(read/write) so it doesn't burn a DVD.
in Windows you can look at the properties of any drive and see what its features are. When you look in device manager, the Textual name of the CD/DVD drive usually adds the +/-RW next to the DVD and or the CD part of the description or the Details and the Hardware_LDS will have the appropriate text there.

It has a DVD/ writer

The DVD Writer/CD Writer is a multipurpose rewriteable drive that can read audio, data, and video files and can record, or write, in both CD and DVD formats. This DVD Writer/CD Writer drive enables you to: Create custom audio, data, and video files that can be recorded onto CDs or DVDs.

What does owner's manual say?