Hi, I have away3d.4.

I’m trying to make a series of 3d lines (please see the image).

Does anyone know of a tutorial that teaches this?

First thing to know, you can’t actually draw a curved line in 3D, but a series of short straight lines that look like a curve.
The class you are looking for is LineSegment.
https://github.com/away3d/away3d-core-fp11/blob/master/src/away3d/primitives/LineSegment.as

This allows you to draw a line between two points in space, with a given colour and thickness.

Good Luck!

I use QuadraticPath for the line path and then a PathExtrude to get a 3D effect and arrow heads.