I would like to see a photo of the existing rear hub, with the cog removed. It looks to me like a proper Campagnolo Nuovo Tipo track hub, and all that's missing is the lockring. You cannot use a bottom bracket lockring, it is threaded wrong (and too big). If you have a track hub, get the lock ring and you'll be good to go.
If it
is a Campagnolo track hub (or Miche, or Gipiemme), be aware that those do not use a standard thread lockring. Rather than a standard 1.29" x 24tpi LH lockring, you'll need a 1.32" x 24tpi LH lockring. From Sutherland's 4th edition: