This one is tricky. First, this particular device is not a dimmer. There are some in wall micros that can do dimming, it’s just this isn’t one of them.
Next, as @Ac7ss said what you can do is going to depend very much on what your existing wiring is. You need to map the circuits. In particular, you need to know exactly where the second master is that this auxiliary talks too. That’s going to make a big difference in what’s possible.
The current set up
First, let me understand the situation. You’re saying you have a double gang box and it has two switches in it. One switch controls the load to fixture A. The second switch is an auxiliary to a third switch, a master, which controls the load to an entirely separate fixture B.
Is that correct? If so, the information you were previously given in this thread may not apply. It all comes down to where that second master is.
The Monoprice dual relay
This relay is designed to control two separate devices on the same circuit (not two separate circuits). This is why there is only one live and one neutral shown in the diagram. The most common set up for this would be lights and an on/off fan in a bathroom. But it could also be lights and a coffee maker in the kitchen.
It is not intended to act as part of a three-way to another circuit. (edited to add as @Navat604 ( who is an electrician) points out below, it may be possible to use one of the two endpoints on this device as part of a three-way, but they all have to be using the same line hot. It’s not just that this is a dual radio device for two separate circuits.)
Zwave threeways
Although zwave threeways can seem complicated at first, it helps if you just don’t think about the nonnetworked wiring at all. It’s just going to work differently.
For a typical three-way set up in zwave you’re going to have the master switch which controls the load to the light/appliance. The auxiliary switch is going to do nothing except send a message to the master switch telling it what to do. That’s it. It will not control any load. This is why many manufacturers call the auxiliary a “remote” or a “dummy.” It just tells the master what to do.
Match the master with an auxiliary specifically designed to work with that model
You always have to match the auxiliary to a master it was specifically designed to communicate with. So in a situation like yours, you’re going to have to replace a third switch as well, the master that the auxiliary communicates with. You always have to replace all of the switches in a three-way/four-way set up when you convert to zwave.
auxiliaries to a Z wave Master can communicate in two different ways
Auxiliaries for a Z wave Master will usually communicate with that master in one of two different ways. Different manufacturers use different methods.
The first method, and the one that you tend to see in high-end switches, is for the auxiliary to communicate wirelessly. It might send a message to the master which then sends a message to the hub, or it might communicate directly to the master. There will be no physical traveler wires used.
This method has the advantage that the master and the auxiliary can be on two completely different circuits, so you can add the auxiliary anywhere that it’s convenient. Also, you will be able to have dimming from the auxiliary if desired. You will see this method in Leviton and Cooper switches, for example. Again, you have to get the auxiliary that matches the master. ( this is also the method that Lutron switches typically use , even though they are not using zwave).
The second common method uses an actual traveler wire between the auxiliary and the master. You still have to use an auxiliary which is designed for use with that master. And the auxiliary still will not control the load to the end device. But there is a physical traveler wire. GE switches use this method.
Why most zwave switches need a neutral
Regardless of the method used for communication between the auxiliary and the master, both the auxiliary and the master have to always have power even when the switch appears to be off. This is so they can communicate to the master. In most cases, this power will come from the neutral.
So, the simplest way to do a three-way with Z wave switches is to get a set specifically designed to work together and which does not require physical traveler wires, and then install them in switch boxes that have a neutral available for each switch. If you do that, it really is pretty easy, in fact it’s easier than many ways of doing a non-networked 3 way because you don’t have to have them on the same circuit and you don’t have to worry about traveler wires.
back to your set up: one master switch for fixture A and an auxiliary for fixture B in a double gang box
In your specific case, as long as there is a neutral in the switchbox available to both of the two switches, I would just put in a master switch for the fixture which is controlled by the master that is already there, and then I would replace the Lutron auxiliary with an auxiliary which is matched to a Z wave Master that is controlling Fixture B, whatever it is. Note that you have to replace that second master as well as any other auxiliary switches tied to it. And then you should be all set.
I would save the relay device that you already have for a situation where you want to control two different end devices on the same circuit. That’s what it is intended for. You will still need a neutral for it, because the neutral is what powers the radio so the relay can hear the next “on command” even when it appears to be off.
If for whatever reason you want to use a relay there, you can do it, but you will be easier to use two separate relays. Most people would use an aeotec micro relay for this.
These can be wired into a three-way using Direct wires to the micro, but to be honest, I would recommend instead setting up a “virtual three-way” where the auxiliary communicates to the hub and the hub communicates to the master. You may have to do it as a virtual if in fact your Lutron auxiliary is not on the same circuit as your existing Lutron master. But in any case note that you were going to need two separate Micros: one for the master A in the box and one for the auxiliary B. And unless you use direct wiring you’re going to also need a third device for master B.
@Navat604 or @dalec or one of the other wiring experts can check this post for me to make sure I didn’t say something backwards or whatever. (I know the devices, but I leave the wiring to the electricians. 
)
The wiring experts may also be able to say whether you can use your auxiliary B with the second endpoint of your current relay. there might also be a way to just get access to the radio.
Anyway, I hope that helps clear up some of the confusion. Since the existing auxiliary is a lutron device, it may have been communicating wirelessly to another Lutron master. You will still need to replace the second master as well as the new auxiliary so that they will be able to communicate to each other. You can’t mix-and-match even if they’re both network switches.
avoiding headaches
You probably already know the following, but just in case:
One) in the US, code does not mandate any particular wire color. So people can and do use any color for any purpose. So you can’t just go by wire colors, you have to actually test every segment of every circuit to know what it’s doing.
- always take before pictures, including of the backs of the switch is where the wires attached to the screws, and label each wire, so you’ll be able to put things back if you run into any problems.