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You can use the heights option

sage: P = posets.DivisorLattice(12)
sage: P.plot(heights = {1: [1,3,4], 2: [2,6,12]})

The keys of the dictionary (here 1 and 2) are the heights and the values (here [1,3,4] and [2,6,12]) are the poset elements to be plotted at this height.