Lines meeting 4 given lines

saddle=Plot3D[x y,{x,-3,3},{y,-3,3},PlotStyle->Opacity[0.8],RegionFunction->Function[{x,y},Abs[x+y]≤2.5&&x y>-2],BoxRatios->{1,1,1}];

saddleNoMesh=Plot3D[x y,{x,-3,3},{y,-3,3},PlotStyle->Opacity[0.8],RegionFunction->Function[{x,y},Abs[x+y]≤2.5&&x y>-2],Mesh->None,BoxRatios->{1,1,1}];

l1:=ParametricPlot3D[{t,0,0},{t,-2,2},PlotStyle->{Thick,Red},PlotRange->2];
l2:=ParametricPlot3D[{t,1,t},{t,-2,2},PlotStyle->{Thick,Red},PlotRange->2];
l3:=ParametricPlot3D[{t,2,2t},{t,-2,2},PlotStyle->{Thick,Red},PlotRange->2];
l4:=ParametricPlot3D[{t,t,1/2},{t,-2,2},PlotStyle->{Thick,Red},PlotRange->2];

Show[saddleNoMesh,l1,l2,l3]

Show[saddle,l1,l2,l3]

Show[saddleNoMesh,l1,l2,l3,l4]

m1:=ParametricPlot3D[{1/Sqrt[2],t,t/Sqrt[2] },{t,-2.2,2.2},PlotStyle->{Thick,Blue}];
m2:=ParametricPlot3D[{-1/Sqrt[2],t,-t/Sqrt[2] },{t,-2.2,2.2},PlotStyle->{Thick,Blue}];

Show[saddle,l1,l2,l3,l4,m1,m2]

Show[l1,l2,l3,l4,m1,m2,PlotRange->2.3,Ticks->None]