I have seen this type of wiring before. It is a standard way to connect Z-wave switches in a 3-way configuration when you have loads that are not incandescent based. You need to be very careful with this type wiring because it is very different from a standard 3-way (your existing Lutron switch). With a standard 3-way, you have two identical switches. One switch connects to line. The other switch connects to load. Between the two switches, two travelers are connected - one of which is always hot. The GE switch works differently. The GE main switch is doing all the work. It has connections to line, load, neutral, and the auxiliary switch through a “traveler”. This traveler is a different sort of traveler than the type used in a standard 3-way. In the GE configuration you have, this wire probably does not carry a voltage. The auxiliary switch merely sends a “sensor” signal to the main switch via the traveler wire to turn it on or off.
I have spent a great deal of time trying to get Z-wave 3-way switches to work in circuits that were previously wired for standard 3-way. Up until now, I was very frustrated because I did not see a way to make it work. However, after looking at your GE switches I see an possible way to make it work as long as you can somehow get a neutral to the main GE Z-wave switch. If you can provide a neutral to the main Z-wave switch, you will be able to power the GE main switch and you will have three wires that run from the main switch to the auxiliary switch. One of these wires could be used to run a neutral line between the main and auxiliary switches. The second line would serve as the “traveler” between the switches. The third wire would run from the load connection on the main GE switch to the load wire in the auxiliary switch box.
If you are going to continue to use incandescent loads in this circuit, I would not use this type of switch. If you want to use a dimmer switch in an incandescent circuit, I would use a Leviton VRI06-1L combined with a VP00R-10 (No LED) Companion dimming switch. They will simply replace your existing switches. If you want a non-dimming switch for an incandescent circuit, then you can use a Leviton VRS05-1L.
This URL will lead you to a spec sheet download for Leviton Visia RF + (Z-wave) switches. It also contains wiring diagrams for the switches:
http://www.leviton.com/OA_HTML/ibcGetAttachment.jsp?cItemId=JpHfVafhIIl5yOOTx6XhDg&label=IBE&appName=IBE&minisite=10251
If you cannot run a neutral to the switch box where you want to install the GE main Z-wave switch and you want to use only fluorescent or LED lamps in the circuit, then I believe that your current GE switch will not work. Z-wave switches need to have power in order to operate. If you have neither a neutral wire or an incandescent light in the circuit (to provides a leakage current), then this GE switch will not function.
Also please note, that even if you can provide a neutral to the GE main switch, the wiring is still very tricky because you have to modify the three wires that run between the main and auxiliary switches for purposes for which they were not originally designed. So if you are not sure of what you are doing, you might want to hire an electrician to do the work for you.
I hope this information proves helpful. Good luck.