@airline-spray
The reason it's not rendering is that you haven't included the Pyro Emitter Tag into the "Simulation Scene" Elements. The simplest solution is to Drag the Cloner's Pyro Tag into the "Elements" Box and rerun the simulation.
Step by step:

1. Rewind, delete and disable caches
2. Select "Simulation Scene" Object and go to "Scene Tab"
3. Drag the Pyro Tag (NOT THE OBJECT) into the "Elements" Box

I had to decrease the sim resolution as my GPU can't handle it, but it did render.

PyroWontRender-1 Fixed.c4d

Scene Nodes has the technology to do that ONLY if you know the Bezier Curve Math required (an algorithm equivalent to what Illustrator does). I personally don't know that math and we don't have a node that can offset the Spline and avoid overlaps.

@emotion-police

...I'd like to know, is there a way to replicate the function of a Lumas shader in the material nodes?

The Lumas shader is Light Based and NOT GI based. It will only react to actual light objects.
Unfortunately, the New Nodes won't support dragging Objects (including Lights) and using their position to create an equivalent to the Lumas Shader.
Your alternative is to use the old Shader Graph (XPRESSO Nodes) and create a material with Only Emission, and drive that emission using a few nodes:

1. Drag any lights in your Graph and get their Global Position.
2. Using a State Node, get the Normal output (the direction of the normal at every rendered pixel) and do a "Dot Product" with the Light's Global Position.
   The dot product of 2 Vectors (normal and Light Position) define the "Perpendicularity" of the two vectors. So if the Normal is pointing towards the light, the product is higher (brighter), while when facing away, it's darker. The result of a Dot Product is just a plain number and NOT a vector.
3. Using a "Change Range" you can define the smoothness of the falloff.

In the attached scene I have used 2 lights and I'm using a Color Layer to mix the result of the 2 calculations by controlling the Mask for each color. The Layer color defines the color of the light.
Although not perfect, it may get you closer to your goal.

https://www.dropbox.com/s/zj5ng9rnp2vvg4w/Lumas%20equivalent%2001A.c4d?dl=0

@command-association
I'm afraid we do not have that functionality in C4D.
This would be a great idea to submit to Maxon.

One thing to note, is that the Control Point count of the Offset spline can NOT be the same as the original one. You can try it in Adobe illustrator with a Spline and Offset and then "Expand" that offset Spline. You will see the number of control points is different.