Based on what others have said, if you reset your Lutron zigbee remote (not the Pico, though), you should be able to get it recognized as a zigbee “thing.” That would be enough to put it on the same network.
So you could use the Remote to toggle lights on and off which were also controlled by smartthings. The only thing is that the smartthings hub wouldn’t know when you use the remote (which Wink does) so they would get out of sync.
That can cause problems because although smartthings does poll the bulbs periodically to get their status directly from the bulbs, in between polls Smartthings might refuse to toggle the bulb because it thought the bulb was already in the state you are requesting.
It’s important it’s one of those things where one person might have the set up and be really happy with it, and another person would be totally frustrated. It really comes down to how often you try to change the bulb state and whether you are controlling bulbs in groups.
You could try and see, but you would need to reset the device before you add it to smart things.
As for the Securifi fob, if you mean the little one that’s about the size of a half-dollar, it does work very well with smartthings, but you need some community contributed code for it. There’s a link off off the list of remotes topic. And again you have to reset it before you can add it to SmartThings. With the community code, you get full “button controller” functionality, which means things don’t get out of sync. It’s a nice little device.