z := x + I y;
f[z_] := (z^3 + 1)/(z + 1);
[Lambda] = 1;
pts = 100;
gre = ContourPlot[
   ComplexExpand[Re[f[z]]], {x, -[Lambda], [Lambda]}, {y, -[Lambda], [Lambda]},
   Contours -> 15, ContourShading -> None,
   ContourStyle -> {{Blue, Opacity[0.5]}}, PlotPoints -> pts];