<< Graphics`Graphics`
<< Graphics`Legend`
ShowLegend[
  LogPlot[
    {S[0.25, LE], S[0.50, LE], S[0.75, LE], S[1.00, LE]}, {LE, 1, 7},
    AxesLabel -> {"Log(E[GeV])", "Shadow" },
    PlotRange -> {.01, 1},
    PlotStyle -> {
    {AbsoluteDashing[{10, 5}], RGBColor[1, 0, 0]},
    {AbsoluteDashing[{5, 10}], RGBColor[0, 1, 0]},
],
  {
    {
      {
        Graphics[{AbsoluteDashing[{
        10, 5}], RGBColor[1, 0, 0], Line[{{0, 0}, {1, 0}}]}],
        "z=0.25"
        },
Graphics[{RGBColor[0, 0, 0], Line[{{0, 0}, {1, 0}}]}],
        "z=1.00"
        }
      },
    LegendPosition -> {1, 0}
    }
  ]