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If you check the manual for the show method you can see there is an argument called cover_labels. You can use this to put labels. I think that if you want to further manipulate the diagram you'll need to check the manual under the show method for DiGraphs, as this is what is being called through the Poset class.

Po=Posets.BooleanLattice(4)
label={}
for (i,x) in enumerate(Po.cover_relations()):
    label[tuple(x)] = i
Po.show(cover_labels=label)

This produces.