Another definition of spruce (in addition to a fir tree and tidying up) seems to deal with deceit, pretence, and bragging, according to my Oxford Concise Dictionary and the Scots Language dictionary site referenced by GUEST,Starship at www.dsl.ac.uk/

That would tie the two lines of the song together:

the advert for "A fine country house shaded gently by trees" and
the lawyer ... "sending me up with spruce in the trees"

Bob