Use LZW31-SN as aux switch?

I have a three way non-neutral wire setup and was curious if I can use one of these dimmers on each end or if I need to buy one of those ge aux switches specifically?

Welcome to the community.

I do not believe you could use two Red dimmers in this application. This is because the non-neutral dimmers require either a load or a neutral.

Let me explain:
You cannot operate two Red dimmers connected together like an aux. You would have to control the load with one dimmer (1).

The other (dimmer 2) would just be a Z-Wave controller talking to the hub. It would not be connected to your light. It would be connected to the no wires on the load output but would be able to communicate. HOWEVER dimmer 2 would have to have a neutral for this to work. Since you have no neutral at either switch your only option is the Aux switch.

But would not the “controller” dimmer have to have a neutral to power the radio?

This is the “no neutral required” switch…does that make a difference?

No, The description “No-Neutral” refers to the wiring when a load is connected.
Every device required two wires; Power In and Power Out. Most often called Line and neutral.

The Red dimmer has a really creative capability. It can use the load as the neutral, but only to power the internal Z-Wave radio and controls.

The 2nd Red Dimmer cannot connect to the load so the only wire would be the line in.

If you can sketch your wiring I can look at it to see if there are other options or a way to wire what you have to do what you wish.

Hint: when I draw sketches like this I use a dashed line for white wires. And you do not need to include the bare wire that goes to each device body.