Also, now that #20343 is in Sage (9.6.beta7). If graphviz is installed and `sage -i dot2tex` as well, one can do:
sage: P = Poset((SetPartitions(4), lambda A,B: A in B.refinements()))
sage: from sage.misc.latex_standalone import TikzPicture
sage: TikzPicture.from_poset(P, prog='dot').pdf()
The dot graphviz program places the nodes in a tree like form. Valid values for prog are ['dot', 'twopi', 'neato', 'circo', 'fdp'], but they do not create as nice pictures:
sage: TikzPicture.from_poset(P, prog='neato').pdf()