Another important point to make in connecting it to Lord Randal is that there is no evidence to show that LR in the English language is any older than about 1790 (according to Child) and Burns supplied this version to Johnson. It could well have been translated into English shortly before that time making My Boy Tammy/Billy older in English.

Fowler, Bronson and others have demonstrated quite convincingly (IMHO) that many of the ballads Child included were products/adaptations of the 18thc.