I have a long line of wood turners, timbermenchants and spade tree makers on one side of the family and Last tree makers on the other.
The word tree was synonmous with wood or wooden part. Thus a spade tree maker made the wooden bits (handle) for spades. A Last tree maker made the wooden lasts for cordwainers to build up their shoes and boots on. (Or to repair them.)
This use of 'tree' is also found in 'treen' the word for small wood items and common until just into the 20C in and around Birmingham. (May have lasted longer elsewhere.)