eqns
       = {x'[t] == s (y[t] - x[t]), 
        y'[t] == x[t] r - y[t] - x[t] z[t], 
        z'[t] == x[t] y[t] - z[t] b}

vals = {s -> 10, b -> 8/3, r -> 99.58}

ini = {x[0] == 0, y[0] == 1, z[0] == 0}

eqns
       = {x'[t] == -y[t] - z[t], y'[t] == x[t] + y[t] a, 
        z'[t] == b + x[t] z[t] - z[t] c}

vals = {a -> 1/5, b -> 1/5, c -> 5.3}

ini = {x[0] == -1, y[0] == 0, z[0] == 0}

sol = 
      NDSolve[Join[eqns /. vals, ini], {x[t], y[t], z[t]}, {t, 0, 200}, 
        MaxSteps -> Infinity]

pl = 
      ParametricPlot3D[
        Evaluate[{x[t], y[t], z[t]} /. sol[[1]]], {t, 195, 200}, 
        PlotPoints -> 2000, PlotRange -> All]

vrmlcurve[fn_, sx_, t0_, t1_, np_] := 
      Module[{strm, 
          cf = (ToString[
                  CForm[SetPrecision[sx[[#1, 2, 0]][#2], 6]]]&)}, 
        strm = OpenWrite[fn]; 
        WriteString[strm, 
          "#VRML V2.0 utf8\nBackground {\n\tskyColor [1 1 1]\n}\n"]; 
        WriteString[strm, 
          "Shape {\n\tappearance Appearance {\n\t\tmaterial Material {\n\t\t\
\temissiveColor 0 0 0\n\t\t}\n\t}\n\tgeometry IndexedLineSet {\n\t\tcoord \
Coordinate {\n\t\t\tpoint [\n"]; 
        Do[WriteString[strm, "\t\t\t\t", cf[1, t0 + i (t1 - t0)/np], 
            " ", cf[2, t0 + i (t1 - t0)/np], " ", 
            cf[3, t0 + i (t1 - t0)/np], ",\n"], {i, 0, np - 1}]; 
        WriteString[strm, "\t\t\t\t", cf[1, t1], " ", cf[2, t1], 
          " ", cf[3, t1], "\n"]; 
        WriteString[strm, "\t\t\t]\n\t\t}\n\t\tcoordIndex [\n\t\t\t"]; 
        Do[WriteString[strm, i, " "], {i, 0, np}]; 
        WriteString[strm, "-1\n\t\t]\n\t}\n}\n"]; Close[strm]]

Timing[
      vrmlcurve["F:\\Mathematica\\Studium\\Praktikum\\Lorentz_99_58.wrl", 
        sol[[1]], 195, 200, 2000]]

pl2 = 
      Plot3D[Evaluate[x y/b /. vals], {x, -20, 20}, {y, -60, 60}, 
        PlotPoints -> 100]

Show[{pl, pl2}, PlotRange -> {{-40, 40}, {-80, 80}, {40, 160}}]