Zwave won’t come into the picture at all, but that doesn’t matter. SmartThings is a multiprotocol platform: as long as smart things recognizes the device as a switch, it doesn’t matter whether that particular device’s communication protocol is Z wave, zigbee, Lutron via the cloud to cloud integration, Wi-Fi via an LAN integration, or anything else that is cloud to cloud: a switch is a switch.
So when smartthings recognizes that that device has come on, that can be the trigger for any other smartthings – controlled events that you want to have happen. Exactly the same as a Z wave switch or a zigbee Switch.
So as @Core_Phx said, it’s all about the events. And as he also mentioned, you do need the Lutron SmartBridge to manage the integration. One smartbridge can handle up to 40 lutron devices.
The only part that’s tricky is that the official SmartThings integration does not recognize the Lutron Picos, which are very handy little remote that can also be wall-mounted and used as auxiliary switches to a Lutron master switch. They are also inexpensive, around $18.
You can use the pico’s with SmartThings, but in order to do so, you have to have the smartbridge pro model instead of the regular model and you also have to set up an additional “server” device as a “man in the middle” integration. It can be done, and there are quite a few community members who are doing it, but it’s much more complex than it would be a smartthings just recognized the pico’s. But it doesn’t.
Anyway, I do indeed like the Lutron’s and have them all over my house. Very well engineered devices. (They also work with HomeKit, which is a plus for me.) I can certainly recommend them as a solution to the no neutral problem, which is also an issue at my house, which was built in the 1950s.
If you do want to stick with Z wave, another alternative is to get the newest generation of the Fibaro micros or some of the Aeotec nano micros. These do not require a neutral in some configurations, but they may require an additional “bypass” device depending on the load on the circuit and the whole thing can get pretty expensive and a bit complicated. But I did just want to mention it because it is an option for those who want to stay with Z wave.