Adding in a call to CheckIfAllUsersReady in the RelayUtpHost within the lobby rate limits, so that if a player disconnects and all remaining players are readied, the countdown will begin. (If and when Wire is integrated, that might obsolesce this.)

Assets/Scripts/Lobby/LobbyAsyncRequests.cs

             private float m_timeSinceLastCall = float.MaxValue;
             private readonly float m_cooldownTime;
             private Queue<Action> m_pendingOperations = new Queue<Action>();
-            private bool m_isHandlingPending = false; // Just in case a pending operation tries to enqueue itself again.
-                if (!m_isHandlingPending)
-                    m_pendingOperations.Enqueue(action);
+                m_pendingOperations.Enqueue(action);
             }
 
             private bool m_isInCooldown = false;
             private void OnUpdate(float dt)
             {
                 m_timeSinceLastCall += dt;
-                m_isHandlingPending = false; // (Backup in case a pending operation hit an exception.)
                 if (m_timeSinceLastCall >= m_cooldownTime)
                 {
                     IsInCooldown = false;
-                        m_isHandlingPending = true;
-                        while (m_pendingOperations.Count > 0)
+                        int numPending = m_pendingOperations.Count; // It's possible a pending operation will re-enqueue itself or new operations, which should wait until the next loop.
+                        for (; numPending > 0; numPending--)
-                        m_isHandlingPending = false;
                     }
                 }
             }

Assets/Scripts/Relay/RelayUtpClient.cs

             // The host disconnected, and Relay does not support host migration. So, all clients should disconnect.
             string msg;
             if (m_IsRelayConnected)
-                msg = "Host disconnected! Leaving the lobby.";
+                msg = "The host disconnected! Leaving the lobby.";
             else
                 msg = "Connection to host was lost. Leaving the lobby.";
 

Assets/Scripts/Relay/RelayUtpHost.cs

                 OnNewConnection(conn, id);
             else if (msgType == MsgType.PlayerDisconnect) // Clients message the host when they intend to disconnect, or else the host ends up keeping the connection open.
             {
-                conn.Disconnect(m_networkDriver);
+                conn.Disconnect(m_networkDriver);
+                m_connections.Remove(conn);
+                LobbyAsyncRequests.Instance.GetRateLimit(LobbyAsyncRequests.RequestType.Query).EnqueuePendingOperation(WaitToCheckForUsers);
+
+                // The user ready status lives in the lobby data, which won't update immediately, but we need to use it to identify if all remaining players have readied.
+                // So, we'll wait two lobby update loops before we check remaining players to ensure the lobby has received the disconnect message.
+                void WaitToCheckForUsers()
+                {   LobbyAsyncRequests.Instance.GetRateLimit(LobbyAsyncRequests.RequestType.Query).EnqueuePendingOperation(CheckIfAllUsersReady);
+                }
             }
 
             // If a client has changed state, check if this changes whether all players have readied.
         protected override void ProcessDisconnectEvent(NetworkConnection conn, DataStreamReader strm)
         {
             // When a disconnect from the host occurs, no additional action is required. This override just prevents the base behavior from occurring.
-            // TODO: If a client disconnects, see if remaining players are all already ready.
-            UnityEngine.Debug.LogError("Client disconnected!");
+            // We rely on the PlayerDisconnect message instead of this disconnect message since this message might not arrive for a long time after the disconnect actually occurs.
         }
 
         public void OnReceiveMessage(MessageType type, object msg)