What @JohnRob said.
Those are BX connectors in the boxes, so the cabling is likely BX. The ground is carried by the metal shield and the metal box is therefore grounded. The ground is carried through on the other side at the breaker box.
I believe the below sketch is what you have. I guessing (educated) in some connections so please verify the wiring to the two cables at Switch A.
If this is indeed the case, I think you can get by with a Non-Neutral installation at Switch A and an Aux at Switch B (as you hoped).
If you can verify the below is correct I’ll try to show how the rewired configuration might be.
John
I agree with your drawing based on what we know, but since the hot is being sent to Switch B, wouldn’t the dimmer have to go there? The black 2-wire at Switch A returns the path to neutral.
I think there may be a way if at the light the LINE and NEUTRAL are swapped thereby sending the LINE to Switch A where a non-Neutral configuration might work.
I haven’t worked it out yet but seems possible. I’d have to think on it a mite, and we need to verify the wiring is what the diagram shows.
Okay guys, first I want to thank you very much for taking the time to help me. Clearly, I am a newbie when it comes to wiring. To try to make things easier, I managed to access the light fixture and I took photos of everything I could possibly think off that may help. For the sake of sanity, I’m going to repost the readings from my multimeter and include the additional readings I took today on switch B. I will need to do this in multiple posts as it will only allow me to post a single photo at a time. Here goes…
Photos of Light Fixture Wiring:
Note that this box has three switches. I made sure that the only wires coming to this switch are red, black and white and I circled those in yellow.
Here are the reading from the multimeter for switch A and switch B. Those reading include when the switches are removed and the wires are exposed from both A and B at the same time, the readings from each location when the switch is removed from the location being measured and the switch is installed in the opposite location both in the ON and OFF positions:
Both Switches Removed:
Switch A:
White: 30v
Red: 33v
Black: 0.1v
Switch B:
White: 30v
Red: 33v
Black: 120v
Measurements taken at location where switch is removed with opposite switch installed and in the ON or OFF position:
Switch A (B On):
White: 37v
Red: 120v
Black: .15v
Switch A ( B Off):
White 120v
Red 45v
Black .15v
Switch B (A on):
White: 22.71v
Red: 0.5v
Black: 120v
Switch B (A off):
White: 0.5v
Red: 28v
Black: 120v
As I mentioned in a previous post, I did find two cables capped together in Switch A. I’ll attach that photo to the bottom of this post.
I hope all of this information helps make some sense of this and I’m sorry for not responding quickly to your posts. I had to wait for the wife and kids to be out of the house before I messed with this again. As my luck would have it, power for our internet is on the same circuit as the one I’m screwing around with and when I shut it off to work on this it makes me everyone’s worst enemy here.
I was happy to have found the constant 120v line in switch B. However, I was hoping that the other two wires in that box would alternate between 0v and 120v as you described in your first post. For a moment, I thought things were starting to make sense but… I’m still lost and completely clueless on where either of the Inovelli or the GE aux should go. Thanks again for your help!
Here is a photo of the inside of the box for switch A:
It looks good. I’m going out tonight but will try to get a sketch going tomorrow. You will have to change the wiring at the light, is this possible?
BTW you should document the current wiring and any changes in case you want to revert to what you have now in the future.
John
In each case I’ve included a bypass which may or may not be required.
There is the wiring for your LZW31 and a dumb 3-Way.
Image removed as it was pointed out a non-neutral installation with a dumb 3-way is not supported.
And for a LZW31 and an Aux:
Doesn’t the LZW31 require a Neutral when used with a dumb 3-way? I was under the impression the only time a 3-way that worked without a neutral was with an Aux switch.
I think you might be correct. But now that you’ve stated it I can see even if the dimmer could steal power through the load, when it “switched” from the “load” connected output to the light to the “traveler” connected to the light it would loose power.
.
Just thinking out loud, I wonder if a bypass from the “Line” to the “Traveler” make it work? Folks, do not try this at home we’re trained professionals who have no idea what other issues this could bring up 
Yep. It’s documented by Inovelli here:
If you DO NOT HAVE A NEUTRAL here are the limitations:
3-Way or Multi-Switch Installation: You can only install this switch in a multi-switch setup with an auxiliary switch such as GE’s or HomeSeer’s and you will not be able to use another smart switch or dumb (existing) switch.
Although our switches can support a non-neutral setup I still recommend a electrician to run the neutral. This is for safety and it also brings up the old wiring to NEC/CE code.
And your homeowners insurance company will love you for that !
Can anyone help me understand what I’m not getting right.
Box A HAS two switches. Both 3 way for different things one for stairs and one for dining room.
Box a has 2 live wires coming in.
Box B is 3 wire romex red black and white that run to box a.
The black wire in box b is hooked up to the common on switch but when I trace wire back to box a I see that the black wire has been capped and connected to the live wire that feeds my stair switch in box a.
I’m trying to install a sonoff mini l
I have it alarmist working but when I flip switch in box b to one position I loose power in box an after a couple seconds
