Example of how to watch a Firestore collection for a list of items inside a custom livedata.

GoalListRepository.kt

package com.aniketkadam.dogether.goals

import androidx.lifecycle.LiveData
import com.aniketkadam.dogether.goals.data.GoalsListLiveData
import com.google.firebase.firestore.FirebaseFirestore
import javax.inject.Inject

class GoalListRepository @Inject constructor(private val firebaseFirestore: FirebaseFirestore) {

    fun getOwnGoals(): LiveData<List<Goal>> =
        GoalsListLiveData(firebaseFirestore)
}

GoalsListLiveData.kt

package com.aniketkadam.dogether.goals.data

import androidx.lifecycle.LiveData
import com.aniketkadam.dogether.goals.Goal
import com.google.firebase.firestore.EventListener
import com.google.firebase.firestore.FirebaseFirestore
import com.google.firebase.firestore.ListenerRegistration
import com.google.firebase.firestore.QuerySnapshot


class GoalsListLiveData(private val db: FirebaseFirestore) :
    LiveData<List<Goal>>() {

    private var listenerRegistration: ListenerRegistration? = null

    override fun onActive() {
        super.onActive()
        listenerRegistration = db.collection("user").addSnapshotListener(eventListener)
    }

    override fun onInactive() {
        super.onInactive()
        listenerRegistration?.remove()
    }

    private val eventListener = EventListener<QuerySnapshot> { querySnapshot, e ->
        if (e == null && querySnapshot != null) {
            value = querySnapshot.toObjects(Goal::class.java)
        }
    }

}

The only important things here,
onActive is when you register your listeners
onInactive is when you unregister them.

Inside your listeners, you should call setValue which is a method on the LiveData class which you're extending, and pass it the value of the type you're listening to.