I planning to use loopback for my back end. Is it possible to have three way data binding feature in loopback(like firebase).
Unless I'm mistaken, Loopback doesn't provide that out of the box, so the simple answer is no.
However, you could accomplish a similar outcome using websockets or a real-time network like pubnub or pusher for example. Here's a walkthrough with angular for three-way data binding from pubnub as a reference.