Just so you know, the “Lutron connected bulb remote” (LCBR) actually doesn’t work with the Lutron SmartBridge. It’s a completely separate device on a completely different protocol, only intended for control of smart bulbs, not for any of the other Lutron devices. It’s the Lutron Picos that require the bridge.
As it happens, the protocol the LCBR is using, zigbee, May be able to connect to A SmartThings hub, it’s just that it’s not really easy and a lot of people report it won’t stay connected. So personally, I would recommend just returning it, but if you do want to play around with it a little more, see the following thread. ( assuming you actually bought an LCBR and not a pico.) But be prepared for a lot of very technical discussion and a lot of “it worked for me.” “It didn’t work for me” conversation going back-and-forth. 