So in the If[evecs==Re[evecs], I want to then change the colour in PlotStyle of the ParametricPlot3Ds (say, green if eval<0, orange if eval==0 and red if eval>0). As you can see, I’ve already tried to add another If statement but it doesn’t quite appear to be doing exactly what I want.

Manipulate[{evals, evecs} =  Eigensystem[({{-\[Sigma], \[Sigma],    0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]], X[[1]], -\[Beta]}})]; GraphicsColumn[{Show[ If[evecs == Re[evecs],   ParametricPlot3D[   Evaluate[ConstantArray[X, 3] + t*evecs], {t, -2, 2},    PlotStyle -> {{If[evals < 0, Green, Red]}}], {}],  Graphics3D[{PointSize[0.025], Red, Point[X]}],  ImageSize -> {275, 275}]}],  Row[{Spacer[60],  Dynamic[Style[  Text@TraditionalForm[    HoldForm[({{x}, {y}, {z}})' ==       Dynamic[Round[({{-\[Sigma], \[Sigma],             0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]],             X[[1]], -\[Beta]}}), 0.01]] ({{x}, {y}, {z}})]],  Medium]]}], Delimiter, {{r, 1, Style["r", Medium]}, 0, 40, .1,  Appearance -> "Labeled",  TrackingFunction -> ((r = #; updateFN[]) &)}, {{\[Beta], 8/3,  Style["\[Beta]", Medium]}, 0, 20, .01, Appearance -> "Labeled",  TrackingFunction -> ((\[Beta] = #; updateFN[]) &)}, {{\[Sigma], 10,  Style["\[Sigma]", Medium]}, 0, 50, 5, Appearance -> "Labeled",  TrackingFunction -> ((\[Sigma] = #;    updateFN[]) &)}, Delimiter, {{X, {0, 0, 0}}, 0, 1,  ControlType -> None}, {{X0, 1,  "Fixed Point:"}, {1 -> "\!\(\*SubscriptBox[\(C\), \(0\)]\)",  2 -> "\!\(\*SubscriptBox[\(C\), \(+\)]\)",  3 -> "\!\(\*SubscriptBox[\(C\), \(-\)]\)"}, RadioButtonBar,  TrackingFunction -> ((X0 = #; updateFN[]) &)}, Delimiter, {evecs,  ControlType -> None}, {evals,  ControlType -> None}, {{updateFN, updateFN},  ControlType -> None}, Delimiter, ControlPlacement -> Left,  AutorunSequencing -> {1, 2, 3, 5},  Initialization :> (updateFN[] := (X = {{0, 0,       0}, {Sqrt[\[Beta]*(r - 1)], Sqrt[\[Beta]*(r - 1)],       r - 1}, {-Sqrt[\[Beta]*(r - 1)], -Sqrt[\[Beta]*(r - 1)],       r - 1}}~Part~X0; {evals, evecs} =    Eigensystem[({{-\[Sigma], \[Sigma],        0}, {r - X[[3]], -1, -X[[1]]}, {X[[2]],        X[[1]], -\[Beta]}})];); updateFN[])] 

Thank you in advance for your help!