So essentially you want to turn a leq-matrix into a LatticePoset and get its Hasse diagram:
sage: M = Matrix([ [ 1, 1, 1, 1, 1 ], [ 0, 1, 1, 1, 1 ], [ 0, 0, 1, 1, 1 ], [ 0, 0, 0, 1, 1 ], [ 0, 0, 0, 0, 1 ] ])