TopologicalSort[
    Graph[Flatten[# /. {l_, ld_} :>
        Map[# -> l &,
         DeleteCases[ld, l]]]]] /. {_TopologicalSort -> $Failed} &@
 {{"des_system_lib", {"std", "synopsys", "std_cell_lib",
    "des_system_lib", "dw02", "dw01", "ramlib", "ieee"}},
  {"dw01", {"ieee", "dw01", "dware", "gtech"}},
  {"dw02", {"ieee", "dw02", "dware"}},
  {"dw03", {"std", "synopsys", "dware", "dw03", "dw02", "dw01",
    "ieee", "gtech"}},
  {"dw04", {"dw04", "ieee", "dw01", "dware", "gtech"}},
  {"dw05", {"dw05", "ieee", "dware"}},
  {"dw06", {"dw06", "ieee", "dware"}},
  {"dw07", {"ieee", "dware"}},
  {"dware", {"ieee", "dware"}},
  {"gtech", {"ieee", "gtech"}},
  {"ramlib", {"std", "ieee"}},
  {"std_cell_lib", {"ieee", "std_cell_lib"}},
  {"synopsys", {}}}