Laudnum Bunches (usually spelled without the second "a" for the dance title) is a lively 6 person corner dance in the Headington Quarry style. Lads a Bunchum is a fairly standard Adderbury dance, often danced in an 8 person set (or longer). There is no similarity between the tunes and the dances and they seem unlikely to be directly related.

By contrast, tunes from different traditions such as Princess Royal or Nutting Girl have obvious similarities, as do some dances with similar tunes that are known by different titles.

I understood that it was at one time traditional/acceptable to put bunches of the soporific herb, laudanum, into a baby's cot to, er... encourage it to sleep quietly. The dance title relates to these bunches of laudanum.

I have no idea of the derivation of Lads a Bunchum, but I always suspected that the name had "changed in the telling" because of the perceived similarity between the two dance names.