I sometimes use the Beam-effect on a non-3D solid:
Add a Beam effect
set the length to 100%
Give it this expression on Starting & Ending Point:
l=thisComp.layer("start or endlayer");
p=l.toComp(l.anchorPoint);
-> change the layer name in the first line to different layers for start and end-point
Adjust the colors, softness and thickness to taste.
If you want the thickness of the line to follow the correct 3D distortion add this expression to Starting and Ending Thickness:
l=thisComp.layer("start or endlayer");
w=length(l.toComp([0,0,0]), l.toComp([0,value,0]));
-> change the layer name in the first line to different layers for start and end-point
Put the layer with the lines in the back of the comp and it should look perfectly 3D, eventhough the lines are not.
If you need mulitple lines, you can duplicate the solid, or duplicate the Beam-effect, but select the option “composite on original” on all but the first beam.